2ₛ + 2ₛ Reactions at Transition Metals Citation Steigerwald, Michael Louis (1984) 2ₛ + 2ₛ Reactions at Transition Metals. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/S0HZ-TF05. https://resolver.caltech.edu/CaltechETD:etd-01032007-142600 Abstract A study of the suprafacial 2 + 2 reaction at transition metal centers is presented. It is demonstrated that this reaction is allowed and proceeds with a low activation energy if the reacting transition metal-to-substituent bond is covalent, nonpolar, and has a large component at transition nickel d-orbital character. These chains are evinced by examination of 2 s + 2 s reactions at M-H bonds. Those systems in which M can use d orbitals show lower barriers to the 2 s + 2 s reaction than those in which M cannot use d orbitals. The importance of the electronic structure of the metal-to-substituent bond is highlighted by a study of dichorotitanacyclopropane. This molecule, being a metallacyclopropane, can undergo 2 s + 2 s reactions which one unavailable to a simple olefin. Studies concerning the importance of 2 s + 2 s reactivity in the organic chemistry of nickel, and in the Ziegler-Natta polymerization of simple olefins are presented. It is suggested that the principle of maximum bonding (the Woodward-Hoffmann rules) implies the conservation of transition metal covalency in low-energy catalytic cycles. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Chemistry) Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemistry Thesis Availability: Public (worldwide access) Research Advisor(s): Gray, Harry B. Thesis Committee: Goddard, William A., III (chair) Grubbs, Robert H. Bercaw, John E. Dougherty, Dennis A. Gray, Harry B. Defense Date: 12 September 1983 Funders: Funding Agency Grant Number Caltech UNSPECIFIED NSF UNSPECIFIED Sun Oil Company UNSPECIFIED Record Number: CaltechETD:etd-01032007-142600 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-01032007-142600 DOI: 10.7907/S0HZ-TF05 Related URLs: URL URL Type Description https://doi.org/10.1021/ja00380a026 DOI Article adapted for Chapter 7.I. ORCID: Author ORCID Steigerwald, Michael Louis 0000-0001-6337-2707 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 12 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 03 Jan 2007 Last Modified: 29 Oct 2025 22:37 Thesis Files Preview PDF (Steigerwald_ml_1984.pdf) - Final Version See Usage Policy. 11MB Repository Staff Only: item control page

2, + 2, REACTIONS AT TRANSITLON METALS Thesis by WCHAEL 1;. STEIGERWALI) In Partial Fulfillment of me Requirements for Be Degree of Doctor of Philosophy CaUlfornia Institute of Technolclgy Pasadena, California 1984 S i pobbe& honineb, phoinde ac sentine vide&un pandub inenhe animo quad 4e gmvLtaXe @tige*:, e qLLihub .id &o.t. caub.id quaqua nothehe et unde Xanta m d i tamquam m a t e b i n pectane c o m t e t , haud v h a g e ~ e n t ,ut nunc pPetrumque videmud q u i d 4.ib-i qLLi6que ve&it neboine e*: quametre nempen cannnLLtane locum, quani onub deponene pobsLt. E x i t naepe Sonad wag& ex aedibub a e , e ~ 4 edunk quem p e h t * r ~ ~ m 4ubi.toque X, nevehtit, quippe h o d d o m a u b q u i henti& a 4 e . CWVLit agem n W ~ 1 0 4ad vLLLam p m e c i p M e t r , auiiLium .tea% qua6.i &me cvrdentibub LmRans; o 4 o L M exXempLo, t e t i g i . t cum tumina vLLLae, aut abLt i n somnum g m v h aXque obLivh qua&, aut e t i a m y v r o p w h e m p e t i t a u e h~v.idiX. Hor 4e qLL.i6qu modO 6t~g.i.t~ a*. quem hcdXcet, ut 6Lt, e6hugehe h a d pox%+ u.t, &g& huehe*: et o d i t , pmptenea motibi q d a caubam non $we*: aegetr; quam bene h i vide&, h mbub qLLi6que 4 e l k X . i ~ natuham phimwn -d.tude& cogno4cme netrum, .tempohid a d d quaniam, non u n i u home, ambigLtituh 4 2 k t U 6 , & quo 4 L t mohtaeibub om& a&, po4.t mohtem quae nes.taX cumque, m e n d a . I sincerely thank the California Institute, the National Science Foundation, and the Sun Oil Company for financial support. I have been a t Caltech a long time. Among the myriad of things I've learned here, I've realized that modern science, and the practice of it, a r e certainly not what I had expected before I came here. The natural philosophy of which Lucretius spoke suffers when its fruits a r e forced to turn a profit--no matter what form that profit may take. Bummer. I a m compelled to judge Caltech. It is an excellent place to realize a scientific training. It is a t best only a fair place in which one may become educated. I look back to thank those who have given me their friendship, encouragement, and support. Dave Evans f i r s t interested me in chemistry--1 don't think he knew what he was doing. Tony Rapp6 has taught me s o much, mostly about the practical side of faith. Ken Doxsee helped m e enjoy my stay here more than he knows. I hope Bosco Lee finds what he's looking for. Bob Grubbs helped m e learn s o much about chemistry. His patience has not been misplaced. Bill Goddard is an amazing man. The ability to appreciate harebrained notions for their redeeming features and thereby to impose some--but not too much--discipline on sometimes unruly thoughts must be treasured. Taking calculated r i s k s is part of the job, but taking calculated leaps of faith puts spirit into the whole thing. Lists a r e odious--one always forgets important people. To all who have added s o much to my life in California go my thanks. I cannot forget the Weenies, especially Barry and Art, who made summertime more than just another season. Very special thinks go Adria who always does s o much to remind me about people and life and being happy. The best thing Caltech ever did for me, by bunches, was to introduce me to Mary. Words of thanks will never suffice. ABSTRACT A study of the suprafacial 2 + 2 reaction at transition metal centers is presented. It is demonstrated that this reaction is allowed and proceeds with a low activation energy if the reacting transition metal-to-substituent bond is covalent, nonpolar, and has a large component at transition nickel d-orbital character. These chains are evinced by examination of 2S + 2s reactions at M-H bonds. Those systems in which M can use d orbitals show lower barriers to the 2s f 25 reaction than those in which M cannot use d orbitals. The importance of the electronic structure of the metal-to-substituent bond is highlighted by a study of dichorotitanacyclopropane. This molecule, being a metallacyclopropane, can undergo 2s + 2s reactions which one unavailable to a simple olefin. Studies concerning the importance of 2s + 2s reactivity in the organic chemistry of nickel, and in the Ziegler-Natta polymerization of simple olefins are presented. It is suggested that the principle of maximum bonding (the Woodward-Hoffmann rules) implies the conservation of transition metal covalency in low-energy catalytic cycles. vi TABLE OF CONTENTS Page Chapter 1: I. 11. 111. IV. V. Introduction Results and Discussion Appendix: Details of the Calculations Tables and Figures References and Notes Chapter 2: I. 11. 111. IV. V. VI. 1 1 + Reactions of D2 with C12TiH , C12TiH and C12SCH Reactions of D2 with Main Group Hydrides Introduction Results Discussion Conclusion Appendix: Details of the Calculations Tables and Figures References and Notes Chapter 3: Dichlorotitanacyclopropane I. Introduction 11. Results and Discussion 111. Conclusions IV. Appendix: ~etailsof the Calculations V. Tables and Figures VI. References and Notes Chapter 4: I. 11. 111. IV. V. VI. 1 1 Reaction of C12ZrH with D2 Introduction Results Discussion Conclusion Appendix: Details of the Calculations Tables and Figures References and Notes Page Chapter 5: I. 11. 111. IV. V. VI. Hybridization of Atomic Orbitals on Transition Metals Shapes of Hybrid Orbitals Bonding to Hybrid Orbitals The Nature of the Chemical Bond Figures References and Notes Chapter 6: VI. VII. VIII. Carbon-Carbon Bond Cleavage in Nickelacyclopentanes 2 + 2, Reactions in the Organic Chemistry of Nickel Previous Work Hypothesis Transphos - 2,ll-bis(dipheny1phosphinomethyl)benzo [clphenanthrene Attempted Synthesis of (transphos)nickelacyclopentane Experimental Section Figures References and Notes Chapter 7: I. 11. Effect of Hybridization on Reactions at Transition Metals Concerning the Mechanism of ZieglerNatta Polymerization of Simple Olefins Isotope Effects on Propagation Rates Appendix: Elaboration on Footnote 17 Conclusion Chapter 1. Reactions of 9with C4TiH+, C12TiH and f&ScH. Introduction The 'Woodward-Hoffmann orbital symmetry rules have had a profound effect on the understanding of organic reactions.' but attempts to generalize these rules to organic reactions mediated by transition metals have not led t o specific results of comparable utility.' I t is generally assumed that there are no particular reactions that are symmetryforbidden for transition metal systems. For example, [2s + 251 reactions such as migratory insertion pervade organometallic chemistry,3 whereas analogous reactions a r e k n o w to be forbidden in strictly organic systems. Our belief (vide +&a) is that the detailed nature of the metal- hydrogen and metal-carbon covalent bond is critical to the process of these now allowed reactions. An appreciation of the transition-metalligand covalent bond is now emerging4 that allows us to go beyond the simple standards of allowed and forbidden and to begin predicting relative rates of particular organometallic reactions. In this paper we outline some recent studies of concerted reactions of transition metals. We find that low activation barriers for reactions such as ti) will result when the M-Z bond is nonpolar and covalent, involving strictIy d-character in the metal center. M-Z 1. X-Y --- an, X-Y ? Our analysis of molecules and their reactions is based on simple valence bond wavefunctions supplemented by ab initio generalized valence bond (GVB) c a l c ~ l a t i o n s .Within ~ this description, a chemical bond is formed by the overlap of two one-electron ~ r b i t a l s and . ~ a reaction results from the delocalization of one or more previously localized bonds across several centers, and the subsequent relocalization t o give the bonds of t h e products. The Pauli principle governs the course of these deloc;zliza!ions, and in so doing provides selection rules for reactivity.' In order t o investigate the nature of these reactive orbiLai deiocalizations in the organometallic: migratory insertion reaction, we have studied the three reactions sho\,in in Scheme 1. M-H J O L D lO.b,C - t -1 20,b.C M H D D I 10,b.C M = (P)CI~T< (bl C12Ti, Ic) C12Sc Scheme I These simple exchange reactions are expected t o be electronically quite similar t o the more traditional 12, + 2,; reactions such as insertion of a n olefin into a meta!-hydrogen bond ( Z : , The study of this sequence war chosen to ar.swer three questions: 1) Docs the iniicatcd exchange proceed with a low activation barrier. and, if so. how' 2) What is the effect of the Lewis hcidity of the metal center on this activa:ion barrier? 3) Vhat is the effect of spectator electrons (such as the unpaired electron of CI2TiH) on this activation barrier? Results and Discussion In order t o answer these questions, we have determined accurate , 8-avefunctions for the reactants (la,b,c) and compared them with analogous aavefunctions for the indicated transition states (2a,b.c). The geometries of these species were optimized and are reporied in Tebles I and TI. Throughout t h ~ sstudy, the chloride Uganda, being simply model a ~ i o n i cligands. were held fixed a t the values shown. The four-center transition states were assumed t o have Ca, symmetry, and the geometries were optimized with tks constrain?. The activation barriers are quoted in Table 111. From Table 111 one sees that these ihree reactions proceed with 10%activation barriers (with that of the titanium cation being conspicuously lovier), and hence the reactions are allowed. Examination of the active orbitals alon;- the reaction path indicate why this is so. Figure 1 shows the four active one-eiectron orbitals as they move fr.om reactants to products. \ye see t h a t the original bond pairs (Ti-H and H-H) a r e retained througho.dt the reaction. .4! the transition state, one of these bonds becomes a three-center bond on the three hydrogens; the other a threecenter bond or, the titanium and its two neighboring hydrogens. As the rezctisn p r ~ c e e i l sto products, these delocalized bonds relocalize t o iorm the bo9ds characler!stic of the products. The change in bond pair overlaps (Table Ii') substantiates our assertion that the two ac:ive bonds are retained throughout these reac:~ons It is critical t o note that thc two three-center bonds of the transition s t a t e are orthogonal t o one another, a s demanded by the Pauii principle. I t is in this ability that transition metals outdo main group elements. Examining the pericyclic 12. + G] cyclodimerization of ethylene (Figure 2), we see that the two active bonds in the reactants (the C-C n bonds) cannot delocalize to give two three-center bonds in the transition state that are mutually orthogonal. Either the two delocalized bonds are not orthogonal (forbidden by the Pauli principle) or one of the bonds is forced to be broken a t the transition state (the definition of a forbidden reaction). I t is the shape and availability of the transition metal d-orbital that allox-s the orthogonal delocalization to occur. Based on these considerations, we believe that the more metal dcharacter in the M-Z bond [Eq. (I):, the lower the activation barrier for the exchange reaction and analogous insertions. This is because any metal s- or p-character in the active bond must be removed on going t o the X . . . M . , . Z three-center bond in the symmetrical transition state. leading to increased activation energy (see Table m,and this change in optimal orbital hybridization about the metal *ill be energetically costly. This contributes to the explanation for the very low barrier for exchange TI the $!12Wj system. * The metai orbital in this Ti-H bond is -?fOZ d in character, %-hereasin the other two cases, the corresponding metal orbital is only 50-70% d (Table I, Figures 1, 3, and 4). In comparing the reaction of (Cl,TiH)+ with Ule isoelectron~cCI&H, we see that the effect of increasing the intrtfinsic Lewis acidity of the metal center is to decrease the barrier height for the exchange reaction. One explanation for this is given above. The more electronegative the metal center, the more d-character in the active bond,' and therefore the lower energy of the transition state. A second point is that the overlap of the ~ K Obonding orbitals in (Cl,TiH)+ is quite low (0.44) compared with that in ClzScH (0.74). This indicates that the TiH bond in (ClZT~H)* is significantly weaker than the Sc-H bond in CIZScH. This would imply a correspondingly iotcer barrier for the exchange reaction. Finally, even t h o q h Hz is not a particularly good Lewis base, a donor/acceptor interaction (to the extent of an additional transfer of 0.21electroc: i:oin the new Hz to the C!~TrH'fragment)stabilizes the cationic transition state Comparison of the exchange reactions oi C12ScH and ClzTiH snov;z the efTec: of the odd electron on titanium. In order to transiorm from the metal bonding orbs-a1 in the reactant to that a t the transition state, the reactant orbital must mix with some of the d-orbital, which is singlyoccupied in the case of Ci2Tiii, but empty in the case of the ClzZcH. Eqiijvder.?ly, the odd electron in C12Ti:H)~D)Zmust be in an orbital the: is orihogonal to the Ii . . . ri . . D and H . . . D . . . D bonds. This orthogo?,&ity requirement results in energetic destsbiiization and is abseat in the ; ~tiiis ; ~ . case oiu calculations indicate that this rrAs~----,f case O ~ C ; ~ S C : H )Ifi is of moderate energetic cost, 4.3 kcal (even though the orbital energy of the si%ly-occa~ied orbits! changes from -0.53;4 hartree in C15TS t o -0.5153 hartree in Cl2TtHJ a destabilization oi 10 1 kcal/mol). He expect that such sptc:a!or d-e1ec:rons may have even &realereffect upon reai- tion biirrirrs in other sysLems. There results may have distinct implications for our appreciation of knwrt org?nometallic processes. For exampie, we expect that the exchange of H for D between Cp2*ZrHzand D ~ , ' the direct hydrogenoiysis of lanthanide alkyl complexes.'0 and the thermolysis of C ~ ~ * T ~ ( C H ~ C X ~ S ) ~ , " proceeds by a direct low-center concerted mechsnism, a s in these model studies. furthermore, these results suggest thet the titanium site in Ziezler-Satia polymerization12 is more active if i t is a cotioni- Ti(K) rather than a neutral Ti(II1). In this way, our work underscores the suggestion that on? of the functions of the Lewis acidic cocatdysir used in Ziegler-Satta pslymerization is t o remove an anionic ligend s x h es CIfrom the sphere of the meid. 13 8 Appendix Details of the Calculations Appendix These calculations were performed a t the fully ab initjo level. All titanium, scandium, and hydrogen orbitals (core as well as valence) were optimized explicitly. Geometries were optimized a t the calculational levels outlined in Tables I and 11. Valence double zeta basis sets were used on the metals, and unsealed triple zeta sets on each hydrogen atom." The chlorine atoms were described by valence minimum basis sets that were optimized for CIZTtHz, and the chlorine core electrons were described by an ab initio effective potential.'5 The geometries of the ClZ?tHS species were optimized using the GVB gradient program of Low and Goddard '' In determining the barrier height (Table 111) we calculated the GVB- PP(2/4) wavefunction a t the saddle point, included the two additional spin eigenfunctions characteristic of a full GVB wavefunction (i.e.. GVBRCI), and then carried out a CI calculation allowing all single excitations from the six GJ'B-RCI configurations to all virtual orbitals. This procedure relaxes all orbital orthogonality and spin-coupling restrictions involved in interactions of the orbitals and is expected to yield accurate barriers. In the limits of the reactant and product species, the above wavefunction reducer to a GVB(1/2) wavefunction on Hz plus the following wavefunction on CI,MH. Starting with CVB-PP(1/2) and includmg the third configuration of the RCl. we include all single excitations into the full virtual space. For CIzScH and ClzTiH+. this reduces to GVB-PP, but for CISTiH there are additional spin-coupling terms arising from the extra electronAs a control, we calculated the barrier for the exchange reaction of H + 4 + HD + D. Uslng t h s method, we calculate a barrier of 14.6 kcal/mof for this reaction. The most accurate calculations available show this barrier to be 9.90 kcal/rno~.~'These comparisons indicate that our calculalions should yield barriers that are systematically "5 kcal/mol hlgh. Table I. Geometries of C4MH. a, b) Mulliken Populations i n M-H bond pair Complex 8 (ClTiCl) r (TiH) r(C1-Ti) M (valence d) M (valence s and p) a) Values in parenthesee a r e not optimized. Other parameters were optimized using a ) ] sigma bond. wavefunction having a correlated [ G v B ( ~ / ~M-H Q b, CZTiH was found to be planar. C4TiH and C4ScH were subsequently assumed to be planar. When the Ti-H bond length was optimized at the Hartree-Fock level, a value of 1.58 A was found. Intrapair correlation is critical in this calculation. Table 11: Geometries of C~M(H)(D),.a, b) -. Complex r: 9 I, (I a) In each case the C4M fragment was held fixed a t the values from the C4MH molecule. b, C, symmetry was assumed for a l l complexes. C, The geometry of CGTi(H)(D), and that of C&SC(H)(D), were optimized using gradient techniques a t the Hartree-Fock level. Owing to the inaccuracy ff of the Hartree-Fock prediction of the Ti-H bond length in C4Ti, this B optimization technique could not be used for C&Ti(H)(D),. This reported geometry results from a point-by-point geometry search at the GVB(2/4) level and is therefore only approximate. The geometry in parentheses is the result of this Hartree-Fock gradient optimization. Table 111. CL,M-H + D2 ----t C4M Reactant Mulli ken Populations Transition State D * . * M a . * HBond BarrierHeight Total on hydrogens in MH, 8 P d Terminal Central 69 STiH 2 kcal/mola) 0.0 0.06 1.09 0.70 0.82 CL,TiH 21.7 kcal/mol 0.0 0.11 0. 72 0.93 0.82 C4ScH 17.4 kcal/mol 0.0 0.13 0.61 1.00 0.80 a) Upper limit; see footnote c), Table 11. Table IV. GVB Pair Overlaps in Active Bonds. P Reactants System Transition State H...M...D H.a.D...D M-H H- H C4TiH 0.44 0.80 0.54 0.84 C4TiH 0.66 0.80 0. 72 0.84 ChScH 0.74 0.80 0.77 0.84 e Figure 1. G I 4 orbi:als for the CI2Tl'-H + D2 -' CIZTlf-D + HD reaction. (i) Reactanis. (ii) Transition state. (iii) Products. Solid lines indicate positive arnplitudz and dzshed lines indicate negative am?!i:.ud~. The spacing bet~:-ex contours is 0.175 a.u. 0 ....... D bond I . . l i e 2 . 1'~:er.c.ob>;,S or';.;:els for ti:e CZ::; + Ci:-;+ -. cyci33;;?:.2 tio:; ( I c . (ii) Trar.:ition state. (iii) Froducts reac- YC - c", S ( h,+,)>O band^ rebu,badldbad2ambp :.hh-Fwbdda Figure 3. G\?3orbithlr describing the Sc-il bond of C12ScH. The spacing bttxeen contours is 0.03 a.u. Figure 4. G1.E o r b i l h : ~di:cribizg thr Ti-H bond of CI2TiH. Tbi. spacing beJ.r:t.-: cc:.:?.--s :,@-I: c References and Notes (1) Woodward, R. B.; R. Hoffmann, R. "The Conservation of Orbital Symmetry"; Academic Press: New York, 1970. (2) Mango, F. D.; J . H. Schachtschneider, J. H. J. Am. Chem. Soc., 1971, 93, 1123-1130; Pearson, R. G. Chem. Brit., 1976, 12, 160. (3) See, for example. Collman, J . P.; Hegedus, L. S. "Principles and Applications of Organotransition Metal Chemistry", C'niversity Science Books: Mill Valley, California, 1980. (4) A. K. Rappe' and W. A. Goddard 111, J. Am. &m. Soc., 1982, 104, 297-299, 448-456, 3287-3294. (5) Goddard 111, W. A.; Dunning, Jr., T. H.; Hunt, W. J.; Hay, P. J. Accts. Chem. Res., 1913, 6, 368-376. (6) Pauling, L. "The Nature of the Chemical Bond", Cornell University Press: Ithaca, New York, 1960. (7) Goddard 111, W. A. J. Am. Chem. Soc., 1972 94, 793-807 (6) In almost all transition metal atoms, single ionization results in the removal of an electron from the valence s orbital rather than from the valence d orbital (Moore, C. E. "Atomic Energy Levels"; National Standard Reference Data Series, NBS 35; U. S. Government Printing Oflice: Washington, DC, 1971.) Therefore, electronegative substituents (e.g., C1) will bond to a transition metal using the more easily ionized valence s orbital of the metal, thereby making a more polar (and stronger) bond. This will have less valence s space (and, consequently, relatively more valence d space) for the electronegative substituents (e.g., H) to use in bonding. In general, higher positive charge on the metal (due either to electronegative substituents or to ionization) will indicate that less valence s and more valence d space will be available for subsequent bonding. Higher positive charge on M also indicates a higher electronegativity at M, and hence our statement in the text. (9) Bercaw, J. E. Advan. Chem. Ser., 1978, 167, 136-148. (10) Evans, W. J . ; Meadows, J. H.; Wayda, A. L.; Hunter, W. E.; Atwood, J. L. J. Am. Chem. Soc.. 1982. 104,2008-2014. (11) Bruno, J . W.;Marks, T. J.; Day, V. W. J. Am. a m . Soc., 1962, 104, 7357-7360. I (12) Cossee. P. J. Cdal..1964. 3. 80. (13) Boor, Jr.. J . "Ziegler-Natta Catalysts and Polymerizations", Academic Press, Inc.: Kew York. 1979. (14) The metal basis sets are from Rappe', A. K.; Smedley, T. A,; Goddard 111. W . A. J. Phys. a m . , 1961, 85. 2607-261 I . The hydrogen basis used is a triple zeta contraction of the Huzinaga (unsealed) six primitive basis. See Dunning, Jr., T. H.; Hay, P. J. In "Modern Theoretical Chemistry: Methods of Electronic Structure Theory", Schaefer 111, H . F., Ed.; Plenum Press: Kew York, 1977; Vol. 3 and references therein. (15: (a) Goddard Iff, W . A.; Rappe', A. K. In "Potential Energy Surfaces and Dynamics Calculations"; Truhlar. D. G., Ed.; Plenum Press: New York, 1981, pp 661-684; (b) Rappe', A. K.; Smedley, T. A.; Goddard 111, W . A. J. Phys. Chem.,1981.65, 1662-1666. (16) Low, J. J.; Goddard Ill, W.A., unpublished results. The GVB gradient program is based on HONDO [Dupuis, M.; King, H. F. J. Chem. Phys.. 1978. 68, 3998-40041; Gaussian 80 (Binkley, J. S.; Whiteside, R. A.; Krishnan. R.; Seeger. R; DeFrees, D. J.; Schlegel, H. B.; Topiol, S. W.; Kahn, L. R.; Pople, J. A.); and the vibrational analysis programs of hlclntosh. D. F.; Peterson, M. R. (Quantum Chemistry Program Exchange #342). (17) Siegbahn, P.; Liu, B. J . Chem. Phys.,1978, 60,2547. Chapter 2. Reactions of & with Main Group Hydrides. I. Introduction For the concerted reactions of simple hydrocarbons, it is well-known (from the Woodward-Hoffmann rules) that the suprafacial 2 + 2 reaction is forbidden.' However, for a number of reactions involving main group metals or transition metals, the simplest mechanisms consistent with experiment invoke cyclic, four-center transition states. Examples include the hydroboration of olefins2 [Eq. (I)] and the Cossee Arlrnan mechanism for Ziegler-Natta polymerization3 [Eq.( Z ) ] . BH3 + CH, = CH-, I %B-@w"2-H (1) Recently we have examined several examples of the four-center reaction at transition metals such as the H/D exchange reaction in Eq. (3).4 In that work we showed that &Ti*-H + D2 -[ '.-...H'. .D]t(&Ti. .....d C+x+.D * (3) to achieve a low activation energy it is critical that the bond t o the transition metal be covalent and nonpolar and involve substantial d-orbital character on the metal. If this situation occurs, the reacting bonds [Ti-H and D-D in Eq. (3)] are retained in the transition state, leading to a low activation barrier. Tkis view that the transition metal mediated suprafacial 2 + 2 reaction will proceed at lower activation energy if the metal-loiigand bond in the reactants (M-H, M-CR3, etc.) is nonpolar is a t variance with the belief that polar bonds are more reactive than nonpolar ones,' and at variance with the notion that a vacant orbital of p character (as in trivalent boron, trivalent aluminum, divalent magnesium, monovalent alkali metals, and so forth) serves the same role in promoting the 2, + 2, reaction as a vacant d orbital at a transition metal.' In order to test these ideas concerning selection rules for 2. + 2, reactions, we have performed a6 initio quantum chemical calculations of activation enthalpies for a set of 2, + 2, reactions [Eq. (4)] involving polar M-H bonds in systems that do not allow the use of valence d-orbitals by the reacting atoms. i M-H .H. D-D e e M H D D L M = Li, Na, K. Rb, HBe, YB,YAL, ClrM, Cu, ClMn We find that ezcept for the case of BH,, the transition state [Eq. (4), structure b] is polar (MfH<), making the reaction look like a hydridetransfer (or heterolytic activation of H,).? Only in the case of BH, is the transilion state [Eq. (4) structure b. M = H,B] nonpolar and covalent. We thus find two limiting cases, the "nonpolar" and the "polar" reactions. where (1) the relative rates of the nonpolar reachons can be related to the valence-s-to-valence-p excitation on M and the ability of this n state of M to form strong n bonds, and (2) the relative rates of the polar reactions can be related to the ionization potential of M. II. Results Using methods described in the Appendix, we calculated the activation barrier heights (Table I) for the reactions in Eq. (4). Here we see that there are two sets of reactions: the allowed reactions (En, i 11 24-34 kcal/mol), and the forbidden reactions (EaCtrr 40 kcal/mol). The objective of our analysis will be to understand what makes one reaction "allo~-ed"and another "forbidden", and to provide ways to estimate the activation energy for a reaction based on spectroscopic properties of the reactants We used generalized valence bond (GVB)' wavefunctions to obtain activation barriers for these reactions. In the GVB model, each chemical bond in a molecule is described by two overlapping, one-electron orbitals, just as in the simple valence bond formalism; however, in GVB calculations, these one-electron orbitals are allowed to optimized their hybridization and delocalization. An an example, the GVI3 orbitals for the H-H bond in H, are shown together with the 1s orbital of H atom in Figure 1. Each orbital in the H-H bond looks similar to but not exactly the same as the 1s orbital of the atom. (In fact, the overlap of a GSrB orbital of HEand an atomic is on the same cent.er is 0.988.)' Thus, the GVB method has the interpretability of simple valence bond and the quantitative benefit of self-consistent field optimization. The atomic nature of GVB one-electron orbitals allows the facile qualitative as well as quantitative description of bond forming and bond breaking processes, and hence this particular orbital description is used. In Figure 2 we illustrate the method, showing the four one-electron orbitals that are active in the H/D exchange reaction between BH3 and 4 [Eq.@)I. ye--H + D-D +. : . . [ . H. D '.' 0'' , , H2f3 H D 0 + (5) The optimal description of the B-H bond shows one electron localized in what is predominantly a 1s orbital on H. ((pzb). and one electron localized in a predominantly sp2hybrid orbital on B, ((pa). These orbitals (pZaand +cZb)have an overlap at 0.83, indicative of a strong bond. The bond in DZ is formed by the overlap (S = 0.80) of the two orbitnls, p,, and (plb Each of these two orbitals is predominantly a localized hydrogen 1s orbital. A t the transition state for this reaction, the pair of orbitals, cp,, and (plb, which started the reaction as the D-D bond, has delocalized over the D-D-H region of the HzB(H)(D), molecule, retaining a high overlap. Similarly, the pair of orbitals ((pa and p a , whch started the reaction describing the B-H bond, has delocalized over the H-B-D region, also retaining a hlgh overlap. The delocalization of covalent bonds at the transition state thus results in two three-center two-electron covalent bonds [bonds 1 and 2 in Pigure Z(ii)j. In contrast, we show the results of our study of the reaction of KH xlth D2 in Figure 3. This reaction involves the reorganization of four active orbitals, (p, and p,b (the D-D bond), and pza and pzb (the KH bond), just as above. A s in the BHS + Dp reaction, the D-D bond delocalizes over the D-D-H region in the transition state. In this case, however, the K-H bond delocalizes not over the H-K-D region but just on the "terminal" H and D atoms. Therefore, the transition state for the KH + DZ reaction looks like K+(Hc), 1, ( ~(qr t I i.e., an ionic bond of K+ to H<,whereas for the H3B + D2 reaction, the transition state is best described as a covalent bond between the HeB radical and the H3 radical. The changes in GVB orbital overlaps in the two active bonds in each reaction studied are shown in Table 11. Our studies of the other eight reactions showed that in each case three of the active orbitals (the two describing the H . , , D . . . D bond and one of the orbitals describing the H . . . M . . . D bond, the orbital distributed uniformly over just the two "terminal" hydrogens) were essentially identical (for example, compare Figures 2 and 3, p,,, rp,,,. and rpza a t the transition states). For this reason we show only the fourth active orbital (plb) for each of these other eight reactions in Figure 4. In order to assess the role of charge in determining the properties of the transition states, the Mullrken populations10 of the atoms of the reactants and of the transition states are shown in Table 111. The parameters describing the optimum geometries of the MHj complexes are reported in Table N together with the geometrical parameters optimized for the reactants (M-H and HZ). The wavefunctions and populations at the transition state should be compared with the corresponding quantities of the reactants (M-H and Ha), as shown in Figure 2 for BHS and in Figure 1 for KH. I t is important to note that the KH bond is found to be quite polar, as is apparent because both orbitals of the KH bond are localized on hydrogen. This is in contradistinction to the case of H2B-H in which one orbital is cectered on H while the other orbital remains on boron. (For comparison, the valence s orbital on K atom and the sp2 orbital on free B H ~ " are shown in Figure 5.) On the other hand, the other orbital of the two-electron bond is essentially a hydrogen 1s orbital in each of the cases we studied. Thus the M-H bond goes from the nonpolar extreme to the polar (M+H-) extreme, based solely on the character of the optimized "M-centered" orbital. In a covalent bond, this orbital is localized on the metal (as in BH3), whereas in an ionic bond it is localized on the H. These "M-centered" orbitals for the various M-H bonds are shown in Figure 6. All of the alkalis (Li, Ka, K. Rb) lead to quite polar bonds; however, the B-H bond is nonpolar while AI-H bond is polar. The Be-H bond is intermediate in polarity between the LiH and BH bonds. Transition metals that cannot use d orbitals in the M-H bonds (dlo Cu and d5 Mn) are quite polar. This can be contrasted with cases such as ClzZrHp (Figure 7)12 where the bond is quite nonpolar and covalent with malnly d character on the metal. A more quantitative measure of these charge transfer effects is provided by the Mulliken populations in Table 111. III. Discussion A. Geometries of the MHs Transition State Perusal of Table TV shows that the geometry changes on going from MH + Hz to the four-center transition state are similar for all cases. The reactive M-H bonds lengthen by 0.1 to 0.2 i, while the H-H bond increases (from 0.74 in ~ 2 ) by ' ~0.31 to 0.36 i.The H-H-H angle in MH3 lies in the range 150-160". These values for r(H-H) and +(H-H-H) should be compared with our calculated values of 0.919 and 180". respectively, for the H3 radicall%nd 1.079 iand 18O0,respectively, for the H; anion.15 Based on the electronic structure of the MH, complexes (see Figures 2, 3, and 41, there is little directed valence toward the H3 unit at M in the MHa complexes, and thus the HMH angle ranges from 46" to 99", imposing no independent requirements on the transition state geometries. The reaction of BH3 is unique. The HBH angle internal t o the exchanging units is significantly larger (99" versus 50" to 80" for the other reaction) than the corresponding angles in all the other exchange reactions. Similarly, the H-H-H angle is significantly smaller than the average(132" versus 145" to 169"). This is easily understood in terms of the electronic structure of thls transition state (vide infra). The boron-centered orbital in the H-B-H bond (Figure 2, pzb of the transition state) shows a great deal of boron p-character. (In fact, removal of the boron p functions from the SCF calculations results in an increase in total energy of 74 kcal/mol. whereas the increase is only 24 kcal/mol for the corresponding exclusion in the case of ~ 2 ~ 1 ~ 3The . ' ~dominance ) of this p character implies a preferred H-B-H angle of 180"; however, this would require the rupture of the H3 unit and thus the cleavage of the original D-D bond, thereby making the reaction forbidden. Thus there is a compromise between maximal H- B-H bonding (180" at boron) and maximal H-H-H bonding (180" at the central H), yielding the 100" angle at boron and the 130" internal bond angle at H. Corollary t o this, comparison of the plots in Figures 2, 3, and 4, the Mulliken populatjons in Table 111, and the geometries in Table IV shows a correlation between the polarization of the XlH3 transition state and the H-H-H angle. The more ionic transition states show the more open geometries as judged by the H-H-H angle. B. E l e c t r o n i c s of t h e MH3 Transitition S t a t e In Figure 8 we show the three one-electron orbitals of H3 at the optimum Cz, geometry of this molecllle..'* Comparison of these orbitals with the orbitals of H2BHs (Figure 2) and KH3 (Figure 3) shows that the two s p i e g e l l6 H-H-H orbitals and one of the u n s p i e g e l H-M-H orbitals in both HzBHs and KH3 are very similar to the three corresponding one-electron orbitals of H3. Since these three orbitals are quite similar for all ten reactions studied, we can understand the electronics of these H-D exchange reactions by examining just the f o u r t h a c t i v e orbital of KHz. I t is this orbital that gives the bonding between the H s fragment and the M center, stabilizes the KHz transition state, and therefore determines the activation barrier for the process. Since the H3 orbital, whch is available for bonding to M, is antisymmetric with respect to the plane bisecting the H-H-H angle (i.e., unspiegel), the orbital on M, to be used in the K-Hs bond, must also be antisymmetric with respect to this plane (unspiegel) in order to have a good bond. These unspiegel orbitals on M are those depicted in Figure 4. These data indicate a convenient dichotomy in the discussion of these 2, + 2, reactions. In the case of H2BH + D2 (Figure 2), the fourth orbital on the transition state ((PZb)is localized significantly on the boron center. This plot as well as the Mulliken populations (Table 111) indicate a nonpolar transition state, HzBHj In all nine other cases, the "M-centered" fourth orbital is not associated viith the center M but rather is distributed equally between the two "terminat" hydrogens, giving rise . to a polar transition state such as 1. The nonpolar and polar transition states %illbe discussed in turn. 1. Nonpolar Transition States a. Electronk Structure In the previous section we intimated that in the 2. + 2, reaction the transition state could be viewed as a complex formed between H3 and M. We pointed out that the fourth active orbital must be an orbital that can overlap the singly- occupied unspiegel orbital of the H3 fragment (7, of Figure 8) if ?he two reactive covalent bonds (M-Hand H-H) of the reactants are to be retained a t the transition state. If this unspiegel fourth orbital can be formed from l o w energy orbitals on the M fragment, and if the overlap between this orbital and the unspiegel orbital of H3 is large enough, a nonpolar three-center (H-M-H) bond can be formed, giving a nonpolar reaction. In earlier work,* we reported such strong nonpolar bonds can be formed in cases where M is a transition metal, if the M-H bond of the reactant has significant d-character on the metal. This occurs because a metal d unspiegel orbital will be available to make the M-H3 covalent bond at the transition state. This metallic d bonding orbi- tal has positive and negative lobes at 90" to one another, thus accornmodating square transition states. The requirement that the Hs fragment be intact a t the transition state [equivalent to the requirement that the H-H (D-D) bond of the reactants be retained] establishes geometrical restrictions on the H-hl-H angle that would seem to exclude s and p orbitals from functioning as the fourth orbital in these 2, + 2, reactions. Figure 2 and Table 111 show that the BH3 + 9 reaction does proceed through a nonpolar transition state, and that the fourth active orbital ( ~ 2 ~ uses ) only p functions on boron. Figures 3 and 4 show that boron is distinctly different from the other cases. Only in the BH2 + Dz reaction is the fourth active orbital localized on the "metal" a t the transition state. The Mulliken population analysis in Table 111 indicates that the HzBH3 transition state is nol polar as are the other nine transition states. The polarization of H2BHs is of the form 2, NOT 3. This is reminiscent of the slight polarization noted for transition metal mediated H/D exchange reactions we reported e a r ~ i e r . ~ The sequence of orbital plots in Figure 2 shows that the B-H and D-D bonds of the reactants are capable of smoothly moving to a pair of threecenter, two-electron bonds a t the H2B(H)(D)2 transition state. The bond pair (qz,,pzb) describes a covalent bond between the singly-occupied orbital of H3 and a n orbital that is substantially a boron 2p orbital (Figure 9). The overlap of the two orbitals constituting this three-center bond is indicative of significant bonding. In Figure 10 we show the plots for the two one- electron orbitals of the n-bond of ethylene.17 Note the general simi- larity between these orbitals and the orbitals (vea and vZb) of the unspiegel bond in (H,B)(H,), especially as these two sets of orbitals difler from the corresponding pair of orbitals in (K)'(H3)- (vZa and v ~ in b Figure 3). The fourth active orbital in (HzB)(H~) (veb of Figure 2) is a boron 2p orbital bonding to the unspiegel singly-occupied orbital of H3 in the same way that the orbital, whlch is essentially a carbon 2p orbital on CH2, is bondin& to a similar orbital on the neighboring CH2 fragment in ethylene, giving rise to the C-C rr bond. In this way we view the three-center, twoelectron bond between H2B and Hg as a rr bond. Thus, the ability of a c e d e r M to sustain the nonpolar 2, + 2, reaction is intimately related to the ability of that center to form strong rr bonds! b. Relative Activation Barriers From Figure 4 it is apparent that while BH3 can undergo a nonpolar 2, + 2, reaction with DO. C12AlH and AlH3 cannot. The unspiegel aluminum 3p orbital is just too diffuse to bond covalently to the unspiegel singlyoccupied orbital of H ~ " (Figure 9). This highlights the general observation that second (and lower) row atoms are incapable of forming strong n bonds. (While ethylene is a remarkably stable molecule, the silicon analog. Sl,H,, shows, at best, a fleeting existence.") Thus the transition state for a nonpolar 2, + 2, reaction will be stabilized (all else being equal) if one of the atoms in tile four-centered complex is able to form strong "r;" bonds, i.e., if M is either a first-row atom (an unsaturated complex of simple ligands about a first-row atom) or one of the set of transition metal centers that is capable of forming dkylidene- type n bonds to CH, ( K = C H , ) . ~ ~This is to say that not only must there be an unused valence orbital on M, but that orbital must have the size and shape to allow a high overlap with the unspiegel singly-occupied orbital of H3. In order to form the required "n b o n d to H3 in Eq. (4), the center M must be in an electronic state that has the orbital of n symmetry (the unspiegel orbital) singly-occupied. At the transition state in Eq. (51, the BH2 fragment is in a configuration that separates to the excited (2B1) state of (bent) BH2, NOT to the ground state ( Z ~ , ) The . interaction between the ground state of HzB and the ground state of HS,given a cyclic geometry, is , respulsiue because the singly-occupied orbital in the ground state of BHZ is spiegel and therefore orthogonal to the unspiegel orbital of Hz. This orthogonality defines the absence of bonding. In Figure 11 we show how the strength of the bond between BHg and H3 may be decomposed conceptually into two fragments; viz., AE1 t AE2, where BE, is the "vertical" strength of the HZB-H~bond, and AE2 is the energy required to prepare 7 the bonding state of BHz (2B,, 6) from the ground state A Thus, when estimating relative barriers for similar 2, t 2, reactions, one may use this a -r rr excitation energy as a guide. For example, a t the geometry characteristic of the (HZB)(Hs) transition state," we calculate the BH2 ( 2 ~ -. 1 '?B1) excitation energy t o be 33 kcal/mol (A& in Figure 1 1 ) . A t an analogous geometrySz2we calculate the ClzB ( 2 ~ +, Q1) excitation energy to be 67 kcal/mol. We believe that the ability of 2Bl (BHz) and ZB, (BClz) to form rr bonds is similar;23 thus we predict that the activation barrier for the reaction in Eq. (6) will be Cli! B-H + L$ - H D . 0 (6) significantly &her than that for the reaction in Eq. (5).24 In a similar way, we calculate the %+ excitation for BeH to be 64 k c a l / r n 0 1 . ~ ~ This observation alone suggests that the 2. t 2, reaction of BeHz with & should be higher in energy than the reaction of BH3 with 4, as observed (Table I). It is interesting to note that this o -. rr excitation can be used to estimate the relative energies of distortion from planarity of a series of reactants M-H. Consider the case of BH3 We can form BH3 by bonding the H atom to either the ground (2A1) or excited (2B1) state of bent BH2. Equation (7) shou-s that bonding to the 2A1 state of BH2 results in the planar geometry of BH3, but that bondmg to the 2B, state of bent BHe results in the highly distorted pyramidal form of B H , . ~ Bending ~ BH, from planar corresponds t o incorporating some fraction of the excited state of BH2. Thus the energy of the excited state gives a gauge of the energy needed to carry out t h s distoriton and vice versa. The hlgher in energy the rr state lies, the more difficult the distortion from planarity. Since the idealized transition state [Eq. (4b)l requires the angular distortion of the M-H bond, the mote dtficult this distortion, the higher the actiuution b a n i e r for the 2, + 2, reaction. Based on these considerations, we can construct estimates for the relative heats of formation of MH3 transition states of the nonpolar type based either on the electronic spectroscopy of M, or on the vibrational spectroscopy (M-H bending mode) of MH. 2. Polar Transition States a. Electronic Shucture Viewing the (k!)(H3) transition state as a bond between the H3 radical and the M radical (in a ,C geometry) is convenient for analysis of the electronic structure of this (unstable) molecule. The "fourth electron" starts out in the bonding orbital on M in M-13, and a t the transition state it forms a two-electron bond with the electron in the unspiegel orbital on HS. In the reactions we characterize as polar, this antisyrnmetric orbital on hl is not sufficiently stable to hold the electron and form a covalent bond with Ha. In these cases the fourth electron is transferred from M to H3 to form a polar M'H; state. Thus the [Mt][H3]- state arises naturally in response to the energetic requirement of maximum bonding in the transition state. Table XV shows that the optimum nuclear angle a t the metal in h!Hs is between 50" and 100" for all cases. Only an orbital on M having high angular momentum (d, f , .... orbitals) can position positive and negative lobes at such small angles to one another. In no cases studied are d orbitals available for bonding to the unspiegel orbital of H3. Therefore, either a three-center prr bond must be formed (as in HZBH3) or electron transfer from M to H3 is demanded. In the KH + De reaction there is no valence d orbital available on potassium, and we do not expect the ZP state of K to form strong n bonds, so the only alternative is to form [Kt]!H~]. In Figure 12 we show the four one-electron orbitals describing H; Comparison of these orbitals with those of KHS substantiates our identification of [K+]:H~:. In all of the cases in Figure 4 we can identify the fourth active orbital of MH, with the diffuse antisymmetric orbital of H; (pZb,Figure 12). Closer examination shows that there is some delocalization back from H; to an unspiegel orbital on M+. For the main group compiexes. this orbital must be p-like (Li 2p, Na 3p, etc.). In all of the main group reactions stu- 41 died, the needed unspiegel orbital is empty in the MH reactant, and may thus be used freely in the MHs complex. The extent of delocalization back from Hf to Mt then depends on the energy of the pri orbital, and the ability of Hf to use this orbital. The energies of the pn orbitals may be estimated from atomic spectroscopy.27 These excitation energies tend to increase as one goes to the left and as one goes down in the periodic table. These energetic considerations suggest the amount of backdelocalization will be greater for Li than for Rb, greater for B than for Al, and greater for B than for Li, in agreement with the results in Figure 3. The ability of Hf to use the M pn orbital relies on the effective size of this pi; orbital and on the size of the MH3 molecule. The effective size of the orbital is merely a gauge of dfiuseness. The more diffuse this orbital, the less fully the Hf orbitals can use it. T h s is simply because the energetic effectiveness of the delocalization is proportional to the overlap of the donor and acceptor orbitals.'' The A1 (3p) and B (2p) orbitals are plotted in Figure 9. From these plots one sees that the A1 3p orbital is much less concentrated in space and thus much less able to overlap the unspiegel orbitals of H;. Thus the same orbital characteristic that makes the nonpolar transition state inaccessible in the reaction a? iUH3 (vide supra) disallows the "unspiegel" backbonding from Hf to H,Mt. The bond lengths in the MH, molecule are critical in determining the extent of back-donation from H; onto the pri orbital of M, owing to the exponential decrease of the overlap of the pn and H; orbitals with distance. These bond lengths are determined by the spatial extent of the valence orbitals, which are in turn determined by the size of the M core orbitals. Since the Li-H bonds are shorter than the Rb-H bonds, the back-donation from H; to Li' is not insigniflcant, but the extent of the analogous donation from H< to Rbt is minimal (see Figure 4). A more direct effect of the core electrons on the rr-backbonding can be seen in Figures 3 and 4 . The four valence orbitals of h!H3 all must stay orthogonal to the core orbitals on M. This places particularly important constraints in the cases of H2.m3and CuH3 where the antisymmetric H< orbitals neatly outline the core region on M. The Pauli Principle-induced corevalence repulsion diminishes the stabilizing effect of H< to K+ delocaljzation It is important to note that the cases showing the strongest r; back donation ( L I H ~ ,Be&, and BH,) are fist-row complexes in which the metallic cores are 1s orbitals. Since there are n o core orbitals of unspiegel symmetry, the Pauli Principle is immediately satisfied with regard to t b s r; backbonding. Therefore, there will a l w a y s be the tendency for activa- tion barriers in these 2 + 2 reactions to be smaller for first-row reactants than for the analogous lower row species (all else being equal). Our results (Table 1) substantiate this. In previous work4 we showed that the presence of transition metal valence d orbitals can render mpoLar 2. + 2, reactions to be allowed. Here we have presented data which show that the 2. + 2, reactions a t ClMnH and Cu-H are both very high in activation energy (i.e.. forbidden) What is the cause of this? The bond in CuH is polar and is observed to involve only a small amount of d character on Cu (Figure 6). Similarly, the fourth orbital of the CuH, transition state uses only a very small amount of Cu d-space (Figure 4). In either case the five d orbitals on copper are Nled and thus cannot be used further. Copper cannot take advantage of the valence d orbitals that separate the transition metals from the main group elements. These two cases emphasize our claim that transition melals can render these 2, + 2, reactions allowed only if the d orbitals can be used effectively during the process. In a similar r a y , the Mn-H bond in ClMn-H is polar, using an sp hybrid orbital on manganese and an s orbital on hydrogen. In the CIMnHs transition state, the "fourth electron" resides in an orbital that has only a small amount of metal character. The case of ClMnH is quite different from, say, that of ClzTiH because the five singly-occupied d orbitals are coupled into a particularly stable hgh-spin (sextet) state (recall Hund's Rule). Bonding to one of these orbital in either ClMnH or CLMnHS would cause an increase in the total electrostatic energy of the complex of 40 kcal/mol because of the Pauli ~ r i n c i ~ l therefore, e;~~ utazation of ds Mn d-like functions is "forbidden" unless the spin state of the complex is changed. In the absence of a lower spin coupling, the Mn-H and MnHs bonds have essentially no d character. Therefore, even though the metallic valence d orbitals have the proper symmetry and spatial extent to stabilize the transition state for the 2. + 2, reaction, they are not used. In this way, the Mn of ClMnH is functionally not a transition metal. In both the reactions (CLMn-H and at Cu-H), polar transition states for the 2, + 2, reaction are observed, making these reactions look like hydride transfers or heterolytic Hz activation. The available unspiegel orbital on the metal is 4prr-like, whch in each case is too diffuse and too far away from the H< fragment to be used in TT back-donation; therefore these reactions behave like high-energy main group reactions.30 b. Relative Activation Baniers Our results indicate that one extreme of suprafacial 2 + 2 reactivity is polar, as in Eq. (8). + M-li + D-D [ ..k $: +M H '..d b 0 : ] .f. 1 .+ I (8) In this case the "metal center" is cationic in the transition state; therefore we claim that the activation barrier for this polar 2. + 2, reaction will be lower when the "metal center" is more cationic in the reactants, i.e., when the M-H bond is'more polar in the MfH- sense. .4s a direct corollary, the activation barrier for the MH + Dz exchange reaction that proceeds through a polar transition state will be lower when the ionization poten- tial of M is lower. Thls explains why the barrier for the exchange reaction at NaH is higher than that for the reaction a t KH and RbH; why the barrier is higher for the reaction at Cl&H than for that a t HzAlH; and why the barriers for the exchange reaction a t CuH and ClMnH are so high relative to the Group IA and Group IIA reaction^.'^ This simple rule must be modified to include the effects of back donation from Hg' to M+ that will tend to stabilize the transition state and therefore lower the reaction barrier. For example, in Table I we find the exchange reaction a t LiH to be 6.3 kcal/mol lower in energy than the corresponding reaction at NaH, despite the fact that IP(Li) > ~ ~ ( h - a ) , ~ ' seemingly voiding our simple claim concerning relative rates and ionization potentials. Reference to Figure 4 will show that there is significantly more n backbonding from H< to Li+ than from H< to Na+, as is expected owing to the greater ability of first-row atoms to form strong n bonds. Thus, the simplest description would say that the activation barriers for the LLH and NaH reactions should be roughly equal, but the intrusion of a slight bit of "nonpolar" reactivity into the polar reaction lowers the LIH + HZ reaction barrier. The separation of the 2. + 2, reactions into two types, polar and nonpolar, is obviously an idealization and each of the reactions described in this work is a mixture of the two extremes. Thus the hydrogenolysis of RbH is clearly a polar reaction, and the hydrogenolysis of BH3 is clearly nonpolar, but the hydrogenolysis of BeHz is less obviously one or the other. in all cases studied, the predictions have been clear, however. If a "metal" center can form the "n-bond" to the antisymmetric, singlyoccupied orbital of Hs (that is, if M is boron or a high-valent early transition metal), then the nonpolar route is accessible. If, on the other hand, M is easily ionized (i.e.. if M is a Group IA metal), then a polar transition state is observed. Finally, if neither of the above requirements is met (e.g.. M-H = CIz.4iH, HzAIH, ClMnH, CuH, HBeH), then the 2, + 2, reaction will have a h g h activation barrier. C. Qualit d i v e Representation of the Transition State Throughout our analysis, we have found it quite helpful to conceptualize the transition state not as a complex of two reacting molecules but as a complex formed between two fragments (M and Ha)whose independent identity lies in a direction perpendicular to the reaction path. In this way we can appreciate the transition state as a molecule (albeit unstable) and understand its electronic structure and energetics with the same cognitive tools used in the study of stable molecules. In the investigation of pericyclic reactions such as the 2, + 2 . reaction, the two reactive fragments will contain delocalized valence bonds. In the present example, the Hs fragment contains a bond that cannot be localized between just two centers. This delocalized valence bonding highlights the synchronous movement of two two-electron bonds in the pericyclic process. The djssection of the transition state into these two fragments is useful because we can examine each separately, qualitatively and quantitatively evaluating the factors affecting their energies. Having understood the separated units, we may then analyze the bonding of the two, which gives the transition state its structure. For example, the (HzB)(H3) transition state is formed by a three-center bond between boron and its two neighbor hydrogens. In order to form this bond, the H2B radical was excited to the unspiegel state and the Ha unit was geometrically distorted so that its unspiegel orbital could overlap the boron orbital effectively. These adjustments of the fragments cost 33 kcal/mol and 12 kcal/mol, respectively. Below we outline how this energetic analysis can be used to extend our results. Similar dissection can be of assistance in envisioning transition states for other pericyclic reactions. i) The transition state for the insertion of olefins into metal-hydrogen bonds32 (vide infra) can be viewed as the bonding of the excited unspiegel state of the metal fragment to be a severely distorted ethyl radical (9). ii) The transition state for the [ 1 , 3 ] sigmatropic shift of an allylic methyl group33 may be viewed as the complex formed between an allylic radical and a (planar) CHS radical (10). iii) The 13.31 sigmatropic shift (Cope and Claisen rearrangements) may be visualized-as proceeding through a transition state formed from two allylic radicals bound to one another via their respective unspiegel orbitals (1l).% ., These diagrams show that this analytical scheme represents a valence bond relative of frontier orbital analysis. Important aspects of these reactions (relative rates, selectivities, stereochemistry, etc.) could be explored by studying the ways in which the independent fragments (ethyl radical, allylic radicals, etc.) can be electronically and geometrically distorted and the energies needed to do so. D. Implications and E z t e n s i m In this work we have described the general features of 2, + 2, reactions carried on in the absence of available valence d orbitals a t the unique center M These studies have all involved the addition of the m n polar reagent 51, to M-H bonds that were polar to a greater or lesser degree. Our studies have shown a spectrum of reactivities from the very polar four-center transition state characteristic of rubidium to the nonpolar transition state of boron. We have shown how the nature of MH will determine the propensity to undergo the exchange reaction with 4. We will now generalize these conclusions to other systems. 1. Alkali M eta1 Alkyls Topologically there is not a great difference between the Li-H bond in lithium hydride and the Li-C bond in a saturated lithium alky134 (see Figure 13). Aside from the obvious steric considerations then, the hydrogenation of LiM [Eq. ( l o ) ] should look much like the hydrogenation of LIR (R = alkyl). The major electronic difference in the 2, + 2, transition state for the direct hydrogenation of LiR is the increased electronegativity of carbon over hydrogen.05 This increased electronegativity implies a greater ability to sustain charge; thus a n y process involving carbanionie behavior at the a carbon in a lithium alkyl will be lower in energy than the corresponding reaction of lithium hydride. Lithlum alkyls are known to react with hydrogen to give alkane and lithium hydride.36 We hold that this reaction proceeds either through a direct four-center transition state analogous to Eq. (4) or through an oligomeric equivalent thereof. Vitale and San ~ i l i p ~have o ~ recently ~ reported evidence that supports the four-membered, direct hydrogenolysis, cyclic transition state. They observe very large and negative values of AS$ for hydrogenolysis of n-octyl l i t h u m with HZ a t 50" s T s 80°C. They interpret this as a suggestion of a highly structured transition state drawing a cyclic, four-membered species. They further observe that addition of n-donor bases (such as TMEDA) leads to substantial rate acceleration. The polar mechanism we invoke in the LiH/D2 reaction is supported by this. Note that the L B 3 transition state is polarized more than is the LiH reactant. Therefore the n-donor base is expected to sta- bilize the transition state more than the reactants, thereby lowering the activation barrier and increasing the reaction rate. It is important to note here that the rate of hydrogenolysis of alkali metal alkyls increases in the order Li < K < Cs. This is directly in line with our prediction that the polar 2, + 2, transition state will be lower in energy if the ionization potential of the metal center is lower.38 The polar mechanism nicely accommodates the essential features of the apparent 2. + 2, reactivity of the alkali metal alkyls. 2. Addition of M-H to Ole& We may use the studies reported here as models for the corresponding reactions of metal hydrides with olefms. Equation (12) indicates the topological similarity of the two processes. K'h~lethe absolute energetics of olefm insertion will be different from the reaction with DO, the general trends will be similar. Consider the analysis of the H/D exchange reactions given in Part B. There we thought of the MH, transition state as the complex formed between H3 and M, and analyzed the stabiiity of the transition state in terms of the type and strength of the bond formed between these two units. A strict analogy for the olefin/metal hydride reaction would analyze the bonding between M and CH~-CH~-H. Immediately one sees an interesting difference between the olefin and HO(D,) reactions: whereas H3 is not a stable molecule, the ethyl radical is (albeit reactive). This should have important consequences for the structure of the reaction coordinate diagram for the olefin insertion reaction. In particular, we expect the transition state to occur earlier in the olefin insertion reaction than it ' fact, the transition state for the does in the H / D exchange r e a ~ t i o n . ~In olefin reaction may occur so early that it would appear as though the transition state for hydroboration, for example, is not a four-center pericyclic state all all but rather the "n-complex" suggested by ~ e h l n e r ~ and ' by IIewar4' [Eq. (13)]. Since the electronic reorganization defining the reaction (spin-recoupling or, equivalently, the delocalization and relocalization of one-electron orbitals) will still be of the pericyclic four-center type, we may use the H/D exchange reactions as general guides in the analysis of the olefin reactions. Before discussing particular olefin reactions in detail, we note that, in general, olefin should react more quickly than HZ with metal hydrides (in a 2. + 2, reaction) for two reasons. Firstly, the strength of the C-C n bond of an olefin is about 61 k ~ a l / m o l , ~ which * is significantly less than the 104 kcal/mol bond of H~.*Thus, one expects that the dihydrogen molecule will usually react more sluggishly. Secondly, the plots in Figures 3, 4, and 5 and the data in Table IV indicate that the dihydrogen moIecule is smaller than the optimum size to make part of a fourmembered transition state, especially in the case of nonpolar reactions where the cyclic bonding nature of the transition state is important. One can see especially in the case of BH3 + Hz that the electronic optimum angle a t boron in HzBH3 is 180'; therefore 2 + 2 substrates that permit a larger internal angle a t boron will react more quickly. Both simple estimates and Dewar's MNDO calculations4' show that an olefin does allow a greater internal angle ( 1 1 6 . 5 * ) . ~ Based on the above arguments, we believe that addition of metal hydrides to olefins will occur by the same spectrum of reactivities, from nonpolar to polar, as the addition of these hydrides t o HO When concerted four-center transition states M-H + "2C-2 - [Eq. (14)], M ............ M ,.$c-cHZ: (14) those involving alkali metals will be polar (cf. Li,NaH, KH,RbH), as will those involving alkaIi earths (cf. BeH2) and those involving transition metals whose valence do orbitals are NOT available a t the transition state (cf. ClMnH and CuH). The addition of RgAI-H across the n bond of an olefin will occur through a much more polar transition state than the corresponding addition of RzB-H. The addition of alkali metal hydrides to olefins is not an important reaction, but the reverse [Eq. (1511 is a common pathwav for the thermolysis of organoalkali metal compounds.48 The four-center transition state for this decomposition has been suggested, and evidence supporting this structure has recently been reported.47 i t is interesting to note that this decomposition follows Zaitsev's ~ u l e , *a rule that is consistent not only with E, elimination but also, in this case, with the polar four-center transition state in which positive charge develops transiently on the p-carbon. The hydroboration2 and hydroalumination4g reactions have been extensively studied and used in organic synthesis. The hydroboration reaction is known to be more facile than the analogous hydroalumination reaction, whch is consistent with our calculated barriers for the exchange reactions with D ~ The . exclusive ~ ~ cis-addition5' observed in both reactions implies an effective four-center transition state. The sense of addition in each case leads to placement of the "hydride" on the more substituted carbon of the incoming ~ l e f i n This . ~ ~ has been attributed both to polarization52a (of the form 3) in the transition state and to steric effects.53 Our results suggest the former to be more important in hydroalumination than in hydroboration, and that the latter effect dominates the directing of hydroboration 3. Addition of Metal Alkyls to Oleflns We combine the previous two sections to discuss the reaction shown in Eq. (16) and concentrate on the difference between trialkyl boron and trialkyl aluminum compounds. As a prelude to the discovefy of transition metal-catalyzed stereoregular polymerization of simple o l e k s , Ziegler discovered that olefins will insert into the Al-C bond of trialkyl aluminum compoundsM [Eq. (16), M=MRZ). Despite the fundamental similarity between the structures and reactivities of aluminum and boron compounds, no such insertion reaction is observed between simple olefins and trialkyl boron compounds,55 thls despite the fact that dialkyl boranes react much more quickly with olefin than do dialkyl a l a n e ~ . ~Our ' studies offer an explanation of this paradox. As mentioned above, the predominant electronic difference between trivalent carbon and hydrogen in compounds of the form M-R !R = alkyl. hydrogen) is the greater electronegativity of carbon. Thus, in any reaction involving a polar transition state [Eq. (17), M-R M\XAR (17) + X- Y one would expect a faster reaction for R = alkyl than for R = H ignoring steric considerations. In contrast to this, steric congestion and directed valence and carbon make frontside attack (insertion) of an olefin a t a metal alkyl bond more difficult. For this reason we expect a strictly nonpolar insertion reaction [Eq. (18)] M-R ..R. A-B '-.A to proceed more quickly for R = H than for R = alkyl, Our results on H I D exchange a t BH, and AIH, show that trivalent boron tends to support nonpolar 2, + 2, reactions and that trivalent aluminum tends t o support poLar 2, + 2, reactions. Since there is not '$polar driving force" to overcome the hampering effect of steric crowding at the transition state, we expect the B-H bond to be much more active than the B-CR3 bond in 2. + 2, reactions. However, since the 2, + 2. reactions a t aluminum are polar, significantly more polar than a t boron, transition state polarization will make the N-CR3 bond relatively more reactive than the B-CRs bond toward incoming olefin. This is an example showing how the bisection of 2. + 2. reactivity into the polar and nonopolar extremes and the determination of which factors affect which reactivity patterns could be useful in the analysis and design of catalyst systems. N. Conclusion Re have examined ten pericyclic 2, t 2, reactions of HZ with a metal hydride. In none of these cases were transition metal valence d orbitals used in the reactants, products, or transition state. We found these fourcenter reactions to be low energy (allowed) for the monomeric alkali metal hydrides, and in each case a polar [M+HS]transition state obtained. We also found a low energy reaction at BH3 that proceeds through a covdezltly bound.rumpolar transition state. Xe found the remaining five reactions to be sufficiently high in energy that we consider them to be "forbidden", even though all bonds are retained throughout each reaction. ITe assert that a lor; ionization potential of M promotes polar 2. + 2. reactions at hi-H and that the ability of M to make n bonds promotes nonpolar 2, + 2, reactions at !+H. These "main group" reactions aflord a useful counterpoint to the migratory insertion reactions of organotransition metal complexes.4 APPENDIX: Details of t h e Calculations A. Basis Sets and Effective Potentials Ravefunctions for species discussed in the text were calculated using the generalized valence bond technique8 and the GVB2P5 These calculations were fully ab initio and all electrons were included in all of the calculations except those cases involving chlorine ligands. In these cases, the ten core electrons on chlorine were replaced by an ab initio effective potntial.57 Throughout these calculations, valence double zeta basis sets were used on the heavy atoms5' and a triple zeta basis set was used on the hydrogen atoms.59 The triple zeta basis was used so that the wavefunction could describe any charge on H (HI. H- or neutral H atom) with equal facility. The valence electrons on chlorine were described using a minimal basis." B. Geometries The geometries of a11 of the active species (i.e., MH and KH3) were optimized. These optimizations were all performed a t the Hartree-Fock (HF) level except the cases of ClMnH and ClMnE, which were performed a t the GVB(1/2) and GV8(2/4) levels, respectively. The geometries of the simple diatomic molecules, of the simple binary molecules (BeH2, BHs, and ALHs), and of the manganese-containing molecules were optirrdzed in a point-by-point fashion, while the geometries of all other molecules were optimized using an HF-based gradient optimization program.61 A CZ,. symmetry was assumed for all MHz complexes. C. Wavejunctions and Activation Barriers A t the optimum geometry of MH, the GVB(1/2) wavefunction in which the M-H bond is described in a GVB sense was calculated. These calculations provided the GVB orbital plots shown in Figures 2, 3, and 6. At the optimum geometry for each MH3 complex, a GVB(2/4) wavefunction was calculated. In this wavefunction the two active bonds (H . . . H . . . H and H . . . hl . . . H) are described by four singly-occupied orbitals. One bond pair is symmetric (i.e., spiegel) with respect to reflection in the plane perpendicular to the plane of the reaction and containing M and the central hydrogen: the other bond pair is antisymmetric with respect to this reflection (unspiegel). O u r studies of the reaction of ClZTlHf with Dz indicated that t h s restriction is a valid one.4 In order to determine activation barriers for the exchange reactions, the total energies of MH + HZ and (M)(HS) are compared; hence it is important to determine calculational schemes that will describe the three species consistently. We have found the following scheme useful. The (M)(H3) species is described by a configuration interaction (CI) wavefunction derived from the GVB(ZI4)-PP wavefunction. The GVB-PP wavefunction was supplemented by the two additional spin eigenfunctions characteristic of a full GVB wavefunction (GVB-RCI). From this set of six spin eigenfunctions, all single excitations into the virtual orbitals were allowed. This results in a small CI (in the case of HZBH3, this gives only 87 spatial configurations). Ths CI wavefunction allows relaxation of all orbital orthogonality and spin-coupling restrictions involved in interactions of the reactive orbitals and is expected to yield accurate barriers. In the limits of reactants and products, this wavefunction reduces to a GVB(lI2)-PP wavefunction on MH and on Hz, except in the case of ClMnH in which there are additional spin recoupling ternis arising from the ds part of the wavefunctions. Total energies for the active species a t the various levels of calculation are reported in Table V. Using this calculation scheme and the simple triple zeta basis on hydrogen, we calculate a barrier of 14.6 kcal/mol for the H + HZ reaction.62 This compares favorably with the best available value. of 9.90 kcal/m01.'~ Inclusion of a set of unscaled p functions on each hydrogen lowered this barrier to 13.3 kcal/mol. Addition of a set of unscaled p functions on the active hydrogen in the BHS and He reaction lowered the activation barrier from 28.0 kcal/mol to 17.5 kcal/mol, but interestingly, the addition of a set of d function on boron lowered the barrier only 0.7 kcal/mol to 16.8 kcal/mol. Re therefore believe that our activation barriers are systematically high by roughly 10 kcal/mol owing to the deficient basis on H, but that the inclusion of d functions in the valence region of the main group centers has a negligible effect. Thus, even when given the chance, the main group atoms do mt use d orbitals. While our values for the activation barriers are thus only approximate in an absolute sense, we believe that the relative activation barriers are reliable. - Table I. Barrier heights for reaction 4. M-H LiH NaH KH RbH Be H, BH3 AlH, ChAlH CuH CUMnH AE (kcal/mol) Table 11. Mulliken populations. lWWm Reactants Li Na K Rb HBe &B &A1 CAA1 CIMn Cu 1 Products Table In. GVB Pair Overlaps for theActive Bonds in the MH + 4 Reactions. GVB Orbital Overlaps MH3 symmetric bond MH3 antisymmetric bond 0.84 0.86 0.83 0.86 0.83 0.86 0.81 0.85 0.84 0.88 0.84 0.87 0.84 0.87 0.84 0.89 0.83 0.87 0.83 0.90 h- 0.82 0.86 Hs 0.86 System M-H Bond LiH3 hH 0.73 KaH3 h'aH 0.69 KH3 KH 0.67 RbH3 RbH 0.66 HBeH3 BeH2 0.82 HzBHs BHz 0.83 732x733 AlHs 0.80 CIZAIHS ClzAIH 0.80 cuH3 CuH 0.72 c1Mn.H~ C Hz W 0.77 0.80 - Table IV. Geometries and Geometry Changes in the Reaction MH + D,. M M-H bond lengtha Transition Reactants State Change H-H bond MH, AI 4 4 b, A, = difference between MH, H-H bond length and H-H length in R, (= 0.742 A) A, = difference between MH, H-H bond length and H-H ltngth in H, f= 0.919 A) a, = difference between MH, H-H bond length and H-H length in Hi (- 1.079 h ) Table V. Final Total Energies a t Relevant Levels of calculation.') System LiHs LiH NaH3 NaH m3 KH RbH3 RbH HBeH3 BeHz HZBHLI BH3 Hp.41H3 MH3 Ci2.4lH3 Ci2AIH CUH~ CuH CIVnH3 ClMnH H2 H H3 Hartree-Fock G V B (/ ~2n) bf RCI+Singles Figure 2. G I B orbitals describing the reaction of BH, with Dz.(i) Reac- tants. (ii) Transition state. (iii) Products. The separation between the contours is 0.05 a.u. pi .::;,..><* ,.:;:i ,,.... ..-. :.:. ; ..:.; ..\.-.......-. :5 ;i.. : ....-._.... ..-. . 'I ::.....t ,........ ,.-.:..., ,," E 1 l a \ ii 0 :,;: :;::t:+::.;: ; ; . .... ::::... .. ,$' ,;;;::.?;,: , .. ....-.*, I.. ds, ; ...p ..,... ...-4'- " a,* ; @ _I I @ Qbs4,,aD bod1 1 Figure 3. G'VB orbitals describing the reaction of KH with 4. (i) Reac- tants. (ii) Transition state. (iii) Products. The separation betweer. contours is 0.05 a.u. Figure 4. Fourth active GVB orbital describing the transition state of the reaction of MH with 9 (see text). The separation between adjacent contours is 0.05 a.u. CCH + Figure 5. Singly-occupied orbitals. (a) The 4s orbital on K atom. The separatiori between adjacent contours is 0.025 a.u. (b) The sprtype orbital in the BHZ radical. The separation betu-een adjacent contours is 0.05 a.u. Singly Occupied Orbitals in K atom and BH, Hi! 8 (2sp hybrid Figure 6. GVB orbital (singly-occupied) on M that participates in the M-H bond in MH.The separation between adjacent contours is 0.05a.u. r 8 @ ';, -*-- 4 t .---, . - -.. * , ,, -*. . * r ,* * +I ' * ,; , ',,* , , ' f . : . * , I I , , . 4 I , , , * % , *I 1 I ,,.-,8 1 I 1 :. . ..-_--- 3 -# .,# ,, # # , -r-- * 1 Figure 9. Atormc valence p orbitals on (a) boron and (b) aluminum. The separation between adjacent contours is 0.05a.u. Figure 10. CLFJ orbitals describing the C-C n bond in ethylene. The separation between adjacent contours is 0.05 a.u. Figure 11. Schematic representation of the energetics of formation of the antisymmetric H - . . B - . . H bond in H2BHS. Figure 12. GVB orbitals describiw the tvio delocalized valence bonds of H;. (a: The spiegel bond. (b) The unspiegel bond. Figure 13. G\B orbitals describing the C-Li bond in methyjlithium. The separat~or.between adjacent contours is 0.05 a.u. References and Notes (1) R. B. Woodward and R. Hoffrnann, "The Conservation of Orbital Symmetry", Verlag Chemie, Weinheim, 1971. (2) H. C. Brown, "Boranes in Organic Chemistry", Cornell University Press, Ithaca, New York, 1972. (3) P. Cossee, Reel. Trav. Chim. Pays- Bas, 85, 1151 (1966); J . Boor, Jr., Macromol. Rev., 2. 115-268 (1967). (4) M. L.. Steigerwald and W. A. Goddard 111, J. Am. Chem. Soc.. in press. (5) R. G. Pearson, "Symmetry Rules for Chemical Reactions", Wiley Interscience, New York, 1976, p. 100. (6) Reference 5, p. 413. (7) See, for example, (a) P. J. Brothers, Frog. Inorg. &em., 28. 1-67 (1981); (b) K. I. Gell and J. Schwartz, J . Am. Chem. Soc.. 100. 3256 (1978). (8) W . A. Goddard 111, T. H. Dunning, Jr., W. J. Hunt, and P. J . Hay, Acc. Chem. Res.. 6.368 (1973). (9) This calculation used a triple zeta basis on hydrogen (ref 59) and a simple GVB(1/2) wavefunction on He. (10) The significance and reliability of Mullrken populations is discussed in E. Steiner, "Determination and Interpretation of Molecular Wave Functions". Cambridge University Press, Cambridge, United Kingdom, 1976, Chapter 6. (11) For these calculations we set 6(HBH) = 120' and r(B-H) = 1.19 d;. This is not very different from the observed values of 131" and 1.18 0 A, respectively. (12) The plots in Figure 7 are for the Zr-H bond in CIZZrHz. Here the Mulliken population on H is 0.97. These hydrogens are not hydridic; hi. L. Steigerwald and W. A. Goddard 111, manuscript in preparation. (13) K . P. Huber and G. Herzberg. "Molecular Spectra and Molecular Structure. IV. Constants of Diatomic Molecules". Van Kostrand, Few York, 1979 (14) Calculations on H3 (Hg) were at the GVB(1/2) [GVB(2/4)', level and restricted to C,, geometries. These geometries were optmized a t the GVB level, using a triple zeta basis on hydrogen (ref 60). (15) In these calculations, only the p functions on B and A1 that were in the plane of the reaction were excluded. The quoted energies are differences in total HF energies for the proper HekIH3 and those with the p functions removed (16) We define the terms spiegel and unspiegei to mean symmetric with respect to reflection in a particular plane and antisymmetric with respect to such reflections, respectively. These terms are convenient generalizations of u and n. The bond betwen M and HJ may be considered to be a n bond with respect t o M but a o bond with respect to HZ; the spiegel/unspiegel nomenclature is precise. (17) The geometry of C,H, was taken from "Landolt-Bbrnstein Numerical Data and Functional Relationships in Science and Technology. Group 11. Atomic and Molecular Physics". Vol. 7; H.-H. Hellwege, Editor in Chief. (18) These plots are of p orbitals on the B and A1 atoms that come from simple HF calculations. See, for example, H. Sakurai, H. Sukaba, and Y. sakadaira, J. Am. Chem. Soc., 104.6156-6158 (1982), and references therein. Transition metal alicylidenes have been defined [R. R. Schrock. Acc. Chem. Res., 12. 98-104 (1979)] and described as nucleophilic. The electronic structure of the M-C interaction has been shown to be that of a metal-carbon (a-n) double bond [A. K. Rappe' and W. A . Goddard 111, J. Am. Chem. Soc., 104,448-456 (1982)j. D This is the vertical excitation with r(B-H) = 1.184 A and 19 = 127.6" (the HZB geometry in HeBH3). At R = 1.19 iand T, = 120' (the H2B geometry in BHS), this excitation is 40 kcal/mol. These excitation energies are differences in simple HF total energies. 0 For BC12, r (B-Cl) was set at 1.70A, and IP(CI-B-CI) was set a t 120" The related problem of cis-trans isomerization in o l e h : the isomerization barrier of (H)(D)C=C(H)(D)is 65 kcal/mol and the barrier in (CI)(H)C=C(H)(CI)is 56.0 kcal/mol (S. W . Benson, "Thermochemical Kinetics", Second Edition, Wiley Interscience, New York, 1976, p 106). The ability of the two boron fragments to form unspiegel bonds should thus be commensurate. If anything, these data suggest the BClp fragment be less likely than BHe to form several bonds, making reaction 7 even less allowed. (a) D. J . Pasto and Z.-2. Kang, J. Am. Chem. Soc., 89.295 (1967); (b) ibid.,90. 3797 (1968). For BeH, r(Be-H) was set a t 1.33 i.This is a single-configuration HF excitation energy. W A. Goddard 111 and L. B. Harding. Ann. Rev. Phys. Chem., 29. 363-396 (1978). (27) C. E. Moore, "Atomic Energy Levels", National Standard Reference Data Series. XBS 35; U . S. Government Printing Office, washington, DC, 1971. (28) L. Pauling, "The Xature of the Chemical Bond". Third Edition. Cornell University Press, Ithaca, New York, 1960, p. 121. (29) The sextet d5 core has a total two-electron energy of 5Jd-* - lo&-#. Bondlng to one of these d orbitals would result in a total twoelectron energy of %&, - 6KdVd.- 4[(Kd-&)/2j. Thus the coulombic = 21 energy, for example, increases by 2Kdd.. For ClMnH, hd. kcal/mol. (30) "Organometallic" reactions such as oxidative addition, reductive elimination, and migratory insertion seem to occur via nucleophile/electrophile routes and organocopper centers. See (a) J . P. Collman and L. S. Hegedus. "Principles and Applications of Organotransition Metal Chemistry". University Books. Mill Valley. California, 1980, Chapter 11. Also, (b) "An Introduction to Synthesis Using Organocopper Reagents", G. H. Posner, Ed., Wiley Interscience, New York, 1980. (31) IP(Li) = 5.390 eV, IP(Na) = 5.138 eV; thus A(IP) = 6 kcal/mol (ref 22) (32) (a) Reference 30(a), p. 294; (b) D. S. Matteson, "Organometallic Reaction Mechanisms of the Nontransition Elements", Academic Press, New York, 1974, Chapter 5. (33) See, for example, P. W. Alder, R. Baker, and J. M. Brown, "Mechanism in Organic Chemistry", Wiley Interscience, London, 1971, p. 249. This is in regard to subsequent suprafacial reactivity a t the Li-R bond. Reference 28, p. 91. Reference 46, p. 190. A. A. Vitale and J. San Filippo, Jr., J. Am, a e m . Soc., 104. 7341- 7343 (1982). . H. Gilman, A . L. Jacoby, and H. Ludeman, J. Am. Chem. S o c . , 60, 2336-2338 ( 1938) (a) G. S. Hammond. J. Am. Chem. Soc.. 77.334 (1955); (b) L. Salem, "Electrons in Chemical Reactions: First Principles", Wiley Interscience, Kew York, 1982, Chapter 2. Perusal of the data of Dewar and McKee (ref 41) shows that this is in fact the case. A t their transition states for hydroboration, the nascent C-H bond has a length of 1.7-1.8;. T. P. Fehlner, J. Am. Chem. Soc., 93.6366-6373 (1971). M. J. S. Dewar and M. L. McKee, Inorg. Chem., 17.1075-1082 (1978). S. W. Benson. "Thermochemical finetics", Second Edition, Wiley Interscience, New York, 1976. p. 106. Reference 42, p. 289 This value is an average of the values found by Dewar and McKee (ref 41). See, for example, (a) A . H. Veefkind, F. Bickelhaupt, and G. W. Klumpp. Recl. Trav. a i m . Pays- Bas, 88, 1058 (19G9); (b) A. H. Veefkind, J. v. d. Schaaf, F. Bickelhaupt, and G. W. Klurnpp. J. Chem. Soc., a e m . Commun., 722 (1971). J. Wakefield, "The Chemistry of Organolithium Compounds", Pergamon Press, Oxford, United Kingdom, 1974, Chapter 15. M.-Y. Li and J. San Filippo, Jr., Organometallics, 2. 554-555 (1963) J . March, "Advanced Organic Chemistry: Reactions, Mechanism and Structure", McGraw-Hill. New York. 1968. p. 767. T. Mole and E. A. Jeffery. "Organoaluminium Compounds". Elsevier. Amsterdam, 1972, Chapter 3. Reference 47, p. 67. Reference 2, Section XIV-6 (a) Reference 2. Section XIV-5; (b) Reference 47. p. 69. F. A. Carey and R. J. Sandberg, "Advanced Organic Chemistry. Part B. Reactions and Synthesis", Plenum Press, Xew York, 1977. p. 101. K. Ziegler, Angew. Chem., 64.323 (1952). Reference 2, Sections XVI-3 and Xb7-12 R. A. Bair, W. A. Goddard 111, A. F. Voter. A. K. Rappe', L. G. Yaffe, F.W. Bobrowicz, W. R. Wadt, P. J. Hay, and W. J. Hunt, GVB2P5 Program, unpublished. See R. A. Bair, Ph.D. Thesis, California Institute of Technology. 19RO; F. W. Bobrowicz and W. A. Goddard Ill, In "Methods in Theoretical Chemistry," H. F. Schaefer 111, Ed., Plenum Press, h'ew York. 1979. Vol. 3, p. 77; H1.J . Hunt, P. J. Hay, and X. A. Goddard 111, J. Chem. Phys., 57, 738 (1972). A. K. Rappe', T. A. Smedley, and W. A . Goddard 111, J. Phys. Chem., 85. 1662 (1981). A . K. Rappe". T. A. Smedley, and W.A. Goddard 111, J. Phys. Chem.. 85.2607 (1981). (59) T: H. Dunning. Jr., and P. J. Hay, In "Modern Theoretical Chemistry: Methods of Electronic Structure Theory", H. F. Schaefer Ill, Ed., Plenum Press, Kew York, 1977, Vol. 3 and references therein. (60) W . A. Goddard I11 and A. K. Rappe', In "Potential Energy Surfaces and Dynamics Calculations", D. G. Truhlar, Ed., Plenum Press, New York, 1981. pp. 661-684. (61) J . J . Low and M'. A. Goddard 111, unpublished results. The GVB gra- dient program is based on HONDO [M.Dupuis, and H. F. Kmg. J. C h ~ mPhys., . 68, 3998-4004 (1978)j; Gaussian 80 (J. S. Binkely. R. A. t+-luteside,R. Krishnan, R . Seeger, D. J . DeFrees, H. B. Schlegel, S. a.Topiol, L. R. Kahn, and J . A. Pople); and the vibrational analysis programs of D. F. Mclntosh and M. R. Peterson, Quantum Chemistry Program Exchange No. 34, Department of Chemistry, Indiana University, Bloornington, Indiana. (62) A t this level of calculation, we find H3 to be linear with r(H1-HZ) 0.919 i (63) P. Siegbahn and B. Liu, J . Chem. Phys., 68. 2547 (1978). = Chapter 3. DichloroCitanacy clopmpane. "If a substance is a hybrid of two or more structures, we migh; r.;turally suppose t h a t its ~hemicalreactions would be those characterisiic of, a t any rate, all the structures which have large weights". -G.W. Wheland "Resonance in Chemistry" I. Introduction The chemistry of the enormous number of transition-metal ole* complexes reported in the literature is quite varied.' For example, in some cases transition metals are known to activate olefins toward nucleophilic attack ( I ) , ~ while in other systems, oxidative cycloaddition (2) ~ c c u r s It . ~is the case that metal systems that facilite reaction (1) do not facilitate reaction (2) and vice versa. In an attempt to determine the electronic reason for the difTerent reactivities of various metal-olefin complexes, we were led to examine whether a given metal-oleiin complex should be regarded that is, an acid/base complex with donation of the C-C x-bonding electrons onto the metal supplemented by backbonding of the metal dr; electron pair into the antibonding orbital of the olefin n bond; or ( j as a metallacyclopropane (2) having two metal-carbon sigma bonds and only a single carboncarbon bond.4 We have concluded that some metal-olefin complexes should be viewed as 1 and others should be viewed as 2, and most importantly those species that are best described by 1 will show reactiiity as in ( I ) , and species that are described as 2 will show reactivity as in (2). We suggest that whether a complex has the form of 1 or 2 depends upon the metal, its oxidation state, the nature of the auxilliary ligands around the metal, and the nature of the olefin. This suggests strategies that one might use in designing systems that rill show one type of reactivity in contrast t o another. Results and Discussion A. Structure of a Metcrllacyc1opropan.e Complexes of the form XgTi(Ci&) O[ = anion h a n d such a s v5- cyclopentadienyl) have been reported to react with added olefin lo give titanecyclopentanes [Eq.(3)15 Inasmuch as the predominance of this mode of reactivity over the others open to these olefin complexes is difficult t o predict using a simple acid/base model of the complexes 1 : we undertook the detailed investigation of their electronic structure. As a model we chose Ck'h(C&) (3). Using the procedure outlined in the Appendix [based on the generalized valence bond (G'C9) method], we optimized t h e geometry of this complex. The resulting geometry is shown in Figure la. This calculated geometry should be compared with the structure of Cp;Ti(C,H,) (4) recently determined by Cohen, Auburn, and ~ e r c a and v ~ shovrn ~ ~ in Figure i b . The theory and experiment agree quite closely (disagreements of 0.02 in Ti-C and C-C bond lengths), indicating that the chlorine ligands in 3 a r e reasonable modcls for the Cp* ligands in 4. 7 We also optimized the geometry of CkTi(&f4) using the Hartree-Fock (HF) method (the generalization of the molecular orbital method) and found the results shown in figure l c (5). This indicates that the that electron correlation eflects included in GVB' must be taken into account for an accurate description of systems such as 3. The optimum valence bond orbihls for the Ti-C and C-C bonds of 3. are shown in f g u r e 2 where we see that the ravefunction has the form of a metalfacycle, 2. Here bond 1 is a bent sigma bond between a d orbital on the titanium and a p orbital on the upper carbon. Similarly, bond 2 is a bent sigma bond between a second titanium d orbital and a p orbital on -the lower carbon. Bond 3 is a bent sigma bond between the two carbons of the CHZCHz moiety. Thus the G I 3 wavefunction describes the electronics of a strained three-membered ring.' The strain in the ring is obvious from Figure 2 because the C-Ti-C angle is seen to be 40" (both calculationally and experimentally), but the angle between the two bonding orbitals ' ~h s situation should be compared on Ti (v,,and p a in Figure 2) is 7 5 ~ . T with our observation that in the unstrained system (Cl2TiHZ,6). the H-Ti-H angle is 75", and the angle between the two Ti-centered bonding orbitals (pla and ~ 2 in , Figure 3) is also 75". The orbitals of Figure 2 should also be compared with the C-C bond orbitals from cyclopropane (figure 4). Here the C-C-Cbond angle is 60°, but the angle between the two bonding orbitals a t the same carbon is 100".ll Our conclusion is that the Ti(C&) complexes (3 and 4) are metallacyclopropanes, not T- complezes. B. Reactivity of a J4etallacyclopropan.e The distinction of an acid-base T-complex 1 from a metallacyclopro- pane 2 is not significant in a practical way unless one can see a clear difference in the reactivities of the two difierent forms. The question then is, what reactivity is expected from the dichlorotitanacyclopropane? Recently vie have examined exchange reactions of Hz with several metal-hydrogen bonds'' [Eq. (4)] and found that the concerted, suprafacial 2 + 2 reaction shown in Eq. (5) is allowed (that is, it has a low activation barrier) if (1) the M-H bond is covalent (little or no charge transfer to the hydrogen or to the metal), and if (2) the metal half of this covalent bond is predominantly d in character. The reason that this pericyclic 2, + 2, reaction leads to a low activation energy (i.e., is characterized by strong bonding in the transition state) is that the metal d orbital has a pattern of nodes that allows both of the active bonds to be retained at the transition state of the reaction. With regard to this nodal pattern, there is no Werence between, for example, the Ti- H bond in ClzTIH (see Figure 5) and the Ti-C bond shown in Figure 2. The electronic structure of the titanacyclopropane and our studies of the 2 + 2 reactions at metals, when taken together, suggest that 3 should undergo reactions as outlined in Eq. (6),where XY is some nonpolar reagent. fxemples of this expected reactivity are shorvn in Figure 6 (assuming favorable heats of reaction). Several of these reactions have been observed by Cohen and Bercaw in the CpZ*Ti(CZH,) (Fgure 7). This agreement between the chemistry expected of a metallacycle and that found for 4 confirms that these Ti(CrH,) comptezes are m e t d l m y cles. C. The Titanium- aefin n Complez In the above sections we argue that ClZ71(CzH,)and Cpe*T~(GH,)should be viewed as titanacyclopropanes. We next must consider whether this .form is significantly different from that of the classical n - c ~ m ~ l e In x.~~ order to explore this issue, we restricted the GVB calculations so that there would be two bonds between the carbon atoms (as in the free olefin) and a lone pair of electrons occupying a d orbital on the metal having the proper symmetry to donate from the metal t o the n* system of the olefin. The geometry preferred for this "Dewar-Chatt-Duncanson"type complex is that of Figure lc. As would be expected, the rrcomplex 1 has a shorter C-C bond and a longer TiC bond than does the metallacycle 2 (compare Figures l a and lc). In fact, the C-C bond length in the ncomplex form (Figure lc) is quite close t o the C-C bond length in Zeise's salt14 (Figure 8),long considered as a typical n-complex. Energetic comparison shows the metallacycle form (at its optimum geometry, Figure la) to be 12 kcal/mol lower in energy that the ncomplex form (at its preferred geometry, Figure lc). This further substantiates our claim that 4 and c ~ ~ ? ' ~ ( Care ~ H best , ) thought of as a metallacycles. D. The Reactivity o j a ri- Complez The optimized G\B orbitals describing the n-complex are shown in Figure 9. Pair 1 (cp,, and cplb) shows a basic C-C n bond delocahzed onto the acidic metal, and Pair 2 (pea and vrb) shows the delocalization of the basic doubly-occupied Ti d orbital into the acidic n* orbital of the olefin. Pair 3 (qS, and qSb)shows the C-C sigma bond that has been distorted by the acid-base bonds of pairs 1 and 2. Note that the simple fourelectron 2 + 2 suprafacial reaction described above is no longer allowed because the abihty of the transition metal to form the reactive metal-carbon "d bond" has been quenched. In this way the "transition-metal" character of the bonding has been eliminated and the "main group" H'oodward-Hoffmann rules apply.I5 These plots indicate that the C-C n bond and the Ti lone pair are still intact. The spin- recoupling that results in the disintegration of these two entities and subsequent formation of two metal-carbon bonds of the metallacycle has not occurred. We view this bonding as the interaction of two "closed-shell" molecules. C1,Ti (singlet) and C,H, (as opposed to the bonding in the metallacyclopropane, which is the interaction of two hqher spin fragments. "triplet" CbTi and "triplet" C&). Ths being the case, the chemistry of the n-complex should be dominated by "closedshell'' processes, i.e., reactions in whch the electrons of a bonding pair delocalize together across the same paths. [This is distinct from the pericyclic reactions in which one member of each electronic pair delocalizes while the other remains localized (ideally) on one center 1.121, It is known that when the central metal is an oxidized late transition metal [ P ~ ( I I ) ,P~(II)," '~ F ~ ( I I ) ~ ' ]the , sense of acid-base bonding is acceptor-metal/donor-olefin. In these cases, the intrinsic Lenis acidity of the metal is transferred to the olefin, and thus the olefin is activated toward nucleophilic attack. Examples of this activation are shown in Figure 10. In cases where this mode of bonding obtains, the geometry of the oleflnic &and is not expected to deviate substantially from that of the free olefin. This is due to the persistence of the double bond between the two carbon atoms. Since this bond remains, the overlap between the two carbon pn orbitals that form the olefinic n bond is stdl required and a short C-C internuclear distance results. Complexes between simple unactivated olefins and highly reduced late transition metal centers (Nio,lQ CO-',~' pton) are also quite well known. The chief mode of reactivity of these complexes is olefin dissociation, and in this way these olefin complexes are usually used simply as sources of low-valent metals in homogeneous reactions.23 These compIexes react at the olefin with electrophiles such a s proton acids, but extensive olefinic reactivity is absent in thcse complexes. These observations, as well as several quantum chemical studies and spectroscopic studies2%e consistent with the bonding in these c~mplexesbeing of the acid/base type, in the sense donor-metal/acceptor-olefin. Complexes of this form are expected to have C-C bond distances that are long relative to that of a normal C-C double bond. [For example, the C-C bond length in (Pp3)2N~(C2H,)is 1.43 compare these with r(C-C) = 1.34 25 and in LizFe(CzH~), is 1.43A 20, , in CzH,.] This may be rationalized either by noting that occupation of the antibonding n* orbital reduces the C-C bond order13b or by noting that more effective stabilization of the metal-centered lone pair is realized if the two participating carbon pn orbitals overlap the two lobes of the doubly-occupied d orbital more. This would tend to open the C-M-C angle more toward 93" (thus lengthening the C-C bond) and bend the CHz units out of the plane of the olefin. E. Metallacycle versus n- Cornplezes In the discussion above, we pointed out that there are two distinct forms for an M(C,H,) complex. 1 and 2. We showed that the metallacycle form is preferred in 3 and 4. Of course, the full wavefunction of such a complex will be a mixture or resonance of these two forms.26 We find the stabilization of this mixing to be 2 kcal/rno12' further indicating that the metallacycle form is preferred. Even so, the less favored n-complex form can play a role in chemistry, but only after paylng a 12 kcal penalty due to loss of the favorable metallacycle character. This situation is analogous to that of the enolate anion, which has two ,important resonance structures, 7 and 8. with their relative importance determined by the character of substituents and solvent.'' Even when more stable, the use of structure 7 alone t o describe the enolate would not explicitly recognize the oxygencentered nucleophilicity of the molecule; similarly, exclusion of 7 from consideration would mask the carbon-centered nucleophllicity. The use of this concept of resonance of molecules is fruitful because each resonance structure has it ox?z characteristic and distinct behavior. By determining which canonical form is more important in a given chemical structure, one may estimate the relative importance of the two manifolds of reactivity.*' This being the case, it is necessary t o come t o an understanding of whch physical characteristics of the constituent parts of a metal-olefin complex increase the importance of one canonical form over the other. In the same way that different chemical environments will enhance the importance of 7 or 0, diderent environments (reaction me&um, ligands, M e r e n t metal centers, etc.) will favor I over 2. To make our theory useful, we must outline rules for estimating the relative importance of 1 and 2. We can state rules for deciding when the metallacycle form will predominate over the complex form: 1) High-Spin Metal Fragment The n-complex form requires a doubly-occupied d orbital on the ~ metal that may backbond into the n* space on the 0 1 e f h . l ~Thus metals that have stable low-spin states (i.e., low-lying states with doubly-occupied d orbitals) will be more likely to form acid-base type complexes. Conversely, metal centers that prefer high-spin coupling of the vaIence d shells (such as d2 l'ln,d2 ~ aand~d2 h, ' b ~ ~will ' be more likely t o form metallacyclopropanes. Thus, early transition m2tals *ill tend to form metallacycles and late metal will tend tc form n complexes.3 1 2) Weak C-C n Bond in the Free Oletin Formation of the metallacyclopropane requires the cleavage of a C-C n bond. Therefore the metallacyclopropane form will be more important as the C-C n bond of the free olefin is weaker. Thus, acetylenes and olefins with strained n bonds (methylenecyclopropane, cyclopropenes, norbornadiene, allenes, e t ~ . ) ~ will ' be more likely t o adopt a metallacycle form than will simple olelins. Also, olefins with electron-~ithdrawingsubstituents that weaken the C-C n bond will favor metallacyclopropane formation.33 Since the C-C rr-bond in &H, is one of the strongest C-C n-bonds known,34 ethylene will be the olefm least likely to form a metallacyclopropane. 3) Strong M-C u Bonds Since the major force stabilizing the metallacyclopropane is the formation of metal-carbon covalent bonds, metal fragments that tend to make stronger covalent bonds will favor the metallacycle form. Thus CI2T1 will favor metallacyclopropane less than will CI2Zr or C12Hf owing to the greater radial extent of the bonding orbitals of CleZr and ~ 1 2 ~ Late f . ~transition ~ metals will favor metallacycles less than wiU corresponding early transition metals for the same reason.35 F. Implications - Khen a complex having the form M(C2Q) is judged by the above cri- teria to be predominantly metallacyclic, it should demonstrate chemistry associated with that of two isolated, and strained, metal carbon bonds. Therefore, we suggest that the oxidative cyclization reaction (2), which has been observed for M = c ~ ~ * z ~ . and ~ ~C ~ C ~ ~should T ~ ~be' viewed IiOT as a six-electron process [Eq.(7)~' but rather as the simpler four-electron insertion process [Eq.(8)]. Furthermore, we suggest that reaction (2) is not oxidative a t all; the "divalent" metal in the metallacyclopropane participates in the pericyclic migratory insertion reactionl2 to give the "divalent" metal in the metallacyclopentane. Why is it that these metallacyclopropanes react with olefins (see Fig. 61,while the corresponding dialkyl complexes do not [Eq.(s)]?~' The beautiful simplicity of the metallacyclopropane form is apparent in the plots of Figure 2. The strain in the three-membered ring, which is manifest in the valence bond description, stimulates the migratory insertion reaction. Cyclopropane itself is stable in the presence of simple olefins o d y because for carbon the 2,+ 2, reaction is forbidden15 [Eq. (l0)l. The presence of the metal a t the apical site and, importantly, the use of the metal valence d- o r b i t a l s in the covalent metal- carbon bond allows the intrinsic strain of the three-membered ring to be relieved by a very simple 2 + 2 reaction. It is important to note that the metal fragments (Cp,*Ti, Cp,*Zr, CpCIZTa,etc.) affording the reaction shown in (2) are all expected to be high-spin d2 species.s0 According to the first rule mentioned in Section II.E, the complex formed between each of these fragments and ethylene should be a metallacyclopropane. There are also several examples in the literature where metal fragments that do not have high-spin d-shells promote "oxidative cycloaddition" to give metallacyclopentanes when they are treated w i t h olefins. Ni(0) and Ir(1) are especially e f f e ~ t i v e (Figure ~ ~ ' ~ ~11). In a similar way, low-valent group WII metals are known to react with 2 equivalents of acetylene to give metallacy~lopentadienes~ (Figure 12). In all of these cases the metal is introduced into the (often catalytic) reaction sequence as a low-valent complex that is transformed t o the higher-valent metallacyclic product. We suggest that the change in valency occurs upon the addition of the first equivalent of olefin (or acetylene) to give the metallacyclopropane (or -propene)33'38 [Eq. (1I)]. Kote that in all of the above cases the active rr-bonds are weak ones (due to strain, electron-withdrawing substituents, or the intrinsic weakness of acetylene ti bonds). This was mentioned above as the second criterion for predicting predominance of a metallacyclic structure over a n-complex form. 11l. Conclusions The (3% ccalculations on C ~ T A ( C ~ &lead ) to a metallacyclopropane resonance structure that predominatess over the n-complex resonance structure. The chemistry expected from this metallacyclopropane form involves 2 + 2 suprafacial reactions with the strained Ti-C bond. This reactivity is consistent with experimental observation. We have emphasized that the metallacyclopropane and n-complex forms are not truly separate and distinct; however, we expect that one form Kill take precedence over the other in any one system. This leads t o the partitioning of the chemistry of olefin complexes into two classes. that of the metallacycle and that of the n-complex. The chemistry of the metallacyclopropane is dominated by & + &-type reactions,'* while the chemistry of the n-complex is dominated by acid-base reactions resulting from enhancement of the electrophilicity of the olefin.' By examining the wavefunction of one metallacyclopropane in detail. we have been able to see the ring strain that is not at all apparent in the n-complex form. We have seen how this ring strain plays an important role in metallacyclopropane chemistry, owing t o the suprafacial 2 + 2 reaction that, although forbidden in main group chemistry, is possible a t a transition metal to carbon covalent bond! APPEXDM: Details of the C a l c u l d ~ A. Basis Sets and Effective Potentials H'e calculated GVB(3/6) wavefunctions for the CI,TI(&)~) complex. The titanium, carbon, and hydrogen centers were described in a fully ab initio, all-electron fashion, using valence double zeta basis sets on each3@ The core electrons (1s32s,2p)on chlorine were replaced with the SHC a b initio core effective potential,40 and the valence electrons on chlorine were described using a minimal basis set optimized for molecular environment^.^^ B. C e o m e t r y Variation During the geometry searches, Ch, molecular symmetry was assumed. This is justified for several reasons. Firstly, all tetra- and divalent fourcoordinate titanium complexes are pseudotetrahedral.41 It seems unlikely that the CbTi(C2H,) complexes would deviate from this. Secondly, Bercaw and co-workers have studied C~Z*T~(CZH,) crystallographically and found that the ethylene moiety occupies two of the "tetrahedral sites" about the titanium atom.5b Finally, our experience with similar cornplexes of titanium [C12RHZ, CLTiH, C l e W + , ClzTi=CH2, and C12Ti(CHz)s] also indicates that there is little force driving the two "organic" ligands out of the plane that bisects the C1-Ti-C1 angle. 10.12 Throughout these calculations, the Ti-Cl bond length was Axed a t 2.328 k and the CI-Ti-Cl angle was tixed a t 142". These are the parame- ters calculated for C ~ ~ T ~ and H ~ "since the chlorine h a n d s are used here singly as model "anionic" ligands, the Axing of their positions is justified. The C-H bonds in the complex were fixed a t 1.091 and not varied. although the angle of depression of the mcthylene units was optimized.lc The geometry of the complex was optimized for the GVB-PP(3/6) level wavefunction in which the motions of three pairs of electrons are correlated. Each pair requires two valence bond-like orbitals so that six orbitals are used for the three pairs (hence, 3/6). These six electrons are the "active electrons" in this complex. This wavefuncUon has the flexibility to describe either the three bonds of a rnetallacyclopropane 9 or the three pairs of a rr-complex (a lone pair on the metal, a C-C sigma bond, and a C-C r bond) 10 The geometry search was conducted as follows: (1) With R(CC) = 1.432 and R(Ti-C) = 2.14 k the angle of depression of the CI& units from the ethylene plane was optimized at 21". (2) With this angle set a t 21" and R(C-C) set at 1.432 A the Ti-C distance was bound t o be 2.181 i. (3) With 0 the angle of depression set at 21" and R(Ti-C set a t 2.181 A the carbonD carbon distance was optimized at 1.460 A. In this way the structure shown in Figure l a was found. [A similar geometry variation procedure using a purely HF (molecular orbital) wavefunction gave the geometry show in in Figure lc.] The G\rB(3/6) wavefunction that was variationally determined is that savefunction described by the orbitals in Figure 2. No symmetry or equivalence r3strictions were placed on the wavefunction to force the metallacyclopropane structure. Using symmetry restrictions, we were able to force the C12Ti(&H.,) system to have a vcavefunction describing the n-complex form. This was done by requiring that two covalent bonds be retained between the two carbon atoms. As expected, the GVB(3/6) (n-complex) ~avefunction prefers the geometry of Figure l c (by 4.5 kcal/mol) over the geometry of Figure la. I t is valuable t o examine the Gt'B orbitals describing these structures in more detail. Recall that in the valence bond formalism a covalent bond results from the overlap of two singly- occupied electronic orbitals, say p, and pb. Also recall that the valence bond wavefunction, h,can be written as a sum of two molecular orbital configurations [Eq.(1211, - qW = (ab + ba) = (a + b)2 - kZ (a b)2 - o2 - h20T , (12) where o and o* correspond to bonding and antibonding localized mofecular orbitals and h - 0.1 for a strong bond (overlap = 0 . 8 ) The ~ ~ GVB pair Iawcrizg, AE, is the energetic destabilization realized in replacing the GVB - pair (oz hzoT) by the one configuration (molecular orbital) term (8). A small overlap of the two GVB orbitals indicates large pair lowering energy, and in t h s case a valence bond description is greatly preferred over the MO description. In Table I we list these calculational results for the GVB(3/6) wavefunctions describing the metallacyclopropane and n-complex resonance structures. For comparison we include the analogous data for the two carbon-carbon bonds in ethylene,43 t h e carbon-carbon bond in ethane,43 the carbon-carbon bond in c y ~ l o p r o p a n ethe , ~ ~titanium-carbon bond in C I , T ~ ( C H ~ ) and ( H ) the , ~ ~lone pair on Ti in ClzTi.45 From these and other data we may generalize t h a t Ti-C bond-s are characterized by bond orbitals having a n overlap of -0.6-0.65. This is significantly smaller than t h e overlap of bonding orbitals in a carboncarbon o bond (-0.8-0.85). Also, t h e inclusion of the second configuration ( u ' ~ )in the molecular wavefunction is energetically twice as important in the titanium-carbon bond as in the carbon-carbon bond. Data in Table I indicate t h a t the Ti-C bonds in the metallacyclopropane a r e quite similar t o the "normal" Ti-C bond in CI~T~(CHS)(H). Contour plots of the orbitals of this Tic bond are shown in Figure 13. Comparison of these orbitals wlth the orbitals describing the Ti-C bond in the metallacyclopropane (Figure 2) shows the bent character of the latter bond. Similar plots of the orbitals of t h e C-C bond in ethane are shown in Figure 14. These two bonding orbitals point directly a t one another, unllke the corresponding orbitals of the C-C bond in cyclopropane (Figure 4). Comparison of the two carbon-carbon bonds with t h e two titanium-carbon bonds shows t h a t t h e r e is t h e same relationship between the two Ti-C bonds a s between t h e two C-C bonds. In this way a n evaluation of these GVB wavefunctions makes the strain in t h e titanacyclopropane apparent. The nonpolarity of t h e Ti-C bonds in both the metallacyclopropane and CIZTi(CHS)(H) is also apparent from the plots of the GVB orbitals. Note that in each case there is one orbital that is centered on the metal atom and one orbital centered on the carbon. As a contrasting example, the two GVB orbitals for the Cr-H bond of the d3 sextet state of C ~ H * are sh0x-n in Figure 15. This bond is polar (Crt + H-) because both orbitals (q, and pb) are centered on the hydrogen. Not surprisingly, this polarity also results in a higher overlap (0.77)in this bond than in a typical nonpolar 1:-H bond (overlap = 0.62 in the Ti-H bond in C121V12). Finally. we can assess the shape of the titanium bonding orbital in the metallacyclopropane by plotting the amplitude of this orbital in the plane perpendicular to the Ti-C-C ring and along one of the Ti-C bond axes. Ths plot is shown in Figure 16. From this it is apparent that the Ti bonding orbital is shaped like a dp orbital, just as in C12Tit-H, ClZn-H, C12N.12, Cl,Ti(CH,)(H), C12Ti(CH2)s. C1,Sc-H. ClzZrIf, and The shape of t h s bonding orbital is critical when evaluating the propensity of this bond to participate in 2 + 2 reactions, as mentioned in the above text. The fact that there is a ring of negative amplitude about the waist of the "dumbbell" of positive amplitude in this orbital means that the 2, + 2, substrate can approach the reaction bond from any azimuthal direction to form the quadrilateral transition state required for the pericyclic reaction. The ravefunction that describes the n-complex form is not surpris- ing. The orbitals in Figure 17 show a doubly-occupied d orbital in the singlet state of C1,Ti. Comparison of these plots with the corresponding plots for the rr-complex form of CIZTi(C2H,) shows only minor changes. The changes observed in the two carbon-carbon bonds in the C2H, unit, when complexed to the metal, are not surprising. These bond orbitals in the n-complex indicate some distortion from the normal double bond in ethylene (Figure 18), but the ring strain is not nearly as clearly demonstrated here as in the metaIlacyclopropene form. Furthermore, it is not clear from the rr-complex wavefunction that the ring strain is actually relieved d o n g the 2 + 2 reaction pathway. In this nay the ring strain, a thermodynamic quantity, can at least qualitatively be related to the kinetics of the 2 + 2 migratory insertion reaction. Table I. Parameters characterizing GVB orbital pairs mentioned in this study. rrvYmm GVB Orbitals Electron Pair Molecule Overlap A€ (kcal/mol) C-C bond Ti-C bond C-C r bond 0.72 12.6 C-C o bond 0.87 6.3 Ti lone pair 0.84 3.1 Ethane C-C bond 0.83 9.4 Cyclopropane C-C bond 0.81 10.0 Ethylene C-C r bond 0.64 9.5 C-C o bond 0.88 6.3 Ti lone pair 0.89 1.9 Ti-C bond 0.64 23.2 ~4 CH2 it 1 CH, C4Ti a /CH, b C4Ti H ' a Reference 45. Reference 44. - ;c: :. 2 C1 0 (3 i= 9 i? x z 4 9) g 2c' 3 8 U 0 m .%! - 5 Q , , g 2, . Q, M 0 k * v s g I-, 0 TY a 'i? g 3 % -J05 W ' i? A 0 Q - , U 01 &. nn0 2-g Figun 2. GVB orbitals describing the valence spece of dichlorotitanacy- clopropane. Spacing between contours is 0.05 a.u. The charecteristic dimension of the plot is 6.0 so. Valence Bonds in Dichlorot itonocyctopropone I Ti-Cl u bond CI - c2 - ~. ., ,.... 6 + I I I I I +le I 1 +I b I Ti-C2 u bond I :,-..--, . ...-. I + ,.--. ..-. :.--.. @ :::::: ; :&-*:.; ..._.-' ...' .:. I 420 IbZb I C2 I a bond CI- .' . : CI Ti c2 - ..----.. <....:::; ; I t .-4. :.-.>,'%' t I u I t ,.;..::::. ', I .'..._.' ,. .--.- , .'.-a +SO I I u ......'- . I t ! +3b Figure 3. Plots of the two Ti-H bonds in C k W t (ref 10). Spacing between contours is 0.05 a.u., and the characteristic dimension of the plots is 6.0 so. Ti- H bonds in CI2TiH2 C-C ubonds in cyclopropane a I bond 1 I I I I Cl - c2 I c3 *. I I I I ..---. +,a . , + , 1 ' b I bond 2 c, - I I .. '.. c3 , ,, c2 - : . -. ., \ I f --*-. +2. I I I I I I I 1 .---, + I ,.-. . ..- . ', , ,\,,' *', ; z:,. --.,, ',<,: I-.. .I._. 1 4 r # *.__-- Figure 4. Plots of two of the C-C bonds in cyclopropane. 2' b R g ~ 5.r GVB orbitals describing the li-Hbond in CW-H. Fig- 8. GVB orbitals describing the valence space of dichlorotitaniurn (ethylene). Spacing between the contours is 0.05 a.u., and the characteristic dimension of the plots is 6.0 h. - Valence bonds in T i a complex - -~ - -- - - - I Ti dy, lone pair .---. I I Cl - I I +.?a I I I 4, I C,-C2 I .,,.----.. ,--.. .. :.: , I c2 - ,.-. .* ',. ,.:,* Cl Ti Q bond I I - 0 I .. .' : : .-,. ,', 0 '..-...,.*-. : .._..... I ;:2:, I --_.I : I I $30 I , Ti: + - =Hz v 3 Figure 11. Some reaction of low-valent Group VlIl metals with olefin hsving weak n bonds. + (bipy) N i (COD) K + (bipy)Ni(COD) + bipy N i (COD) CI Ir (COD) + - T- (P4) Ni + =*= 3 bipy Ni ---) - bipy N $ clIre bipy Ni ___c + higher oligomers L C I I r L 2 (N2) + 2 R C = CR -- CI- R Figure 12. Some reactions of low-valent Group VIlI metals with ace- tylenes. Figure 13. GVB orbitals describing the Ti-C bond in Q'h(H)(CHs). Spacing between the contours is 0.05 a.u., and the characteristic dimension of the plots is 6.0 .c. -- - - Kgurc 14. G W orbitals describirq the C C bond in ethane. Kgure 15. CVB orbitals describing the C r H bond in CrH. Fig= 16. Plot of the Ti-centered GVB orbital in the Ti4 rr bond in dichlorotitanacyclopropsnc. The plane of this plot i s perpendicular to the plane of the Ti-C-C ring and contains the 'liand C a t o m of the bond. n g 17.~Lone pair on ( b a t ) nq. Figure 18. GVB orbitals describing the n bond in ethylene. The spacing between the contours is 0.05 a.u.. and the characteristic dimension of the plots is 6.0 Q,. References and Notes (1) (a) "Transition Metal Organometallic Chemistry in Organic Synthesis", H. Alper, Ed., Academic Press, New York, 1976, Vol. 1; (b) M. L. H. Green, "Organometallic Compounds. The Transition Elements", Chapman and Hall, London, 1968, Vol. 1, Chapter 1; (c) S. D. Ittel and J. A. Ibers, Adv. Organornet. Chem., 14.33 (1976); (d) G. Henrici-Olive' and S. Olive', "Coordination and Catalysis", Verlag Chemie, Weinheirn, 1977; (e) J. P. Collman and L. S. Hegedus. "Principles and Applications of Organotransition Metal Chemistry", University Science Books, Mrll Valley, California, 1980, Chapter 3. (2) See, for example, ref lc, Chapter 12, and references therein. (3) (a) R. R. Schrock. S. McLain, and J. Sancho. %re Appl. Chem., 52. 729 (1980); (b) G. Erber and K. Kropp, J. Am. Chem. Soc., 101.3659 (1979); (c) D. R. McAlister, D. K. Erwin, and J. E. Bercaw, ibid., 100, 5966 (1978); (c) A. P. Fraser, P. H. Bird, S. A. Bezman, J. R. Shapley, R. White, and J. A. Osborn, *id., 95, 597 (1973); (e) J. X. McDermott, M. E. Wilson, and G. M. Whitesides. ibid.,98,6529 (1976). (4) The question of n complex versus metallacycle is not a new one. See (a) M. J. S. Dewar and G. P. Ford, J. Am. Chem. Soc., 101, 783 (1979); (b) T. A. Albright, R. Hoffmann, 3. C. Thibeault, and D. L. Thorn, aid., 101, 3801 (1979); (c) B. h e r m a r k , M. Almemarte, J. Almlsf, J.-E. Bhckvall, B. Roos, and ti. stog;, ibid.,99,4617 (1977). (5) (a) See ref 3(e); (b) S.A. Cohen, P. R. Auburn, and J. E. Bercaw, J. Am. Chem. Soc., 105, 1135 (1983); (c) S. A . Cohen, Ph.D. Thesis, Cal- ifornia Institute of Technology (1982). 140 (6) See, however, (a) F. D. Mango and J. H. Schachtschneider, J. Am. Chem. Soc., 93. 1123 (1971); (b) R. G. Pearson, "Symmetry Rules for Chemical Reactions", Wiley-Interscience, New York, 1976, p. 423; (c) J. W. Lauher and R. Hoffmann, J. Am. Chem. Soc., 98, 17291742 (1976). (7) Using [EA(x) + R(M 1 ] = a(X) as a gauge of the propensity for X to form ionic bonds to M, and using R(Ti-Cp) = 2.08 [G. Fachinetti, C . Floriani, F. Marchetti, and M. Mellini, J. Chem Soc., Dalton Trans., 1398 (1978)], r(Ti-C1) = 2.328 (this work), EA(C1) = 3.62 eV [H. Hotop and W. C. Lineberger, J. Phys. Chem. Ref. Data,4, 539 (1975)!, and EA(C,H,) = 2.2 eV [H. N. Rosenstock, K. Draxl, B. W. Steiner, and J. T. Herron, ibid.,6, 736 (1977)], one sees that a(C1) = 9.8 eV and a(Cp) = 9.1 eV. Thus the tendency of Cp and C1 to form ionic bonds is similar, and the gross features of the electronic structure of metal complexes with these ligands should be similar. (8) W. A. Goddard 111, T. H. Dunning, Jr., W. J. Hunt, and P. J. Hay, Acc. Chem. Res., 6, 368-376 (1973). (9: S. W.Benson, "Thermochemical Kinetics", Wiley-Interscience, New York, 1976, Second Edition, p. 60. (10) A. K. Rappe' and W. A. Goddard 111, J. Am. Chem. Soc., 104, 297 ( 1982). (11) This angle is measured from the plots shown m Figure 6 and is the angle between the lines of maximum amplitude of the two orbitals on the same center. (12) M. L. Steigerwald and W. A. Goddard 111, J. Am. Chem. Soc., in press. R. A. Love, T.F. Koetzle. G. S. B. Williams, L. C. Andrews, and R. Bau, Inorg. CZem.. 14. 2653 (1975). R. B. Woodward and R. Hoffmann, "The Conservation of Orbital Symmetry", Verlag Chemie, Weinheim, 1971. G. W. Parshall, "Homogeneous Catalysis", Wiley Interscience, New York, 1980, Chapter 6 and p. 25. N. Belluco, "The Organometallic and Coordination Chemistry of Platinum", Academic Press, New York, 1974, p. 374. M. Rosenblum, Acc. Lhem. Res., 7,122 (1974). (a) K. Jonas, K. R. Pbrschke, C. Kriiger, and Y.-H. Tsay, Angew. Chem. Int. Ed. Engl., 15. 621 (1976); (b) P. W. Jolly and G. Wilke, "The Organic Chemistry of Nickel", Academic Press. New York, 1974, Vol. 1. (a) K. Jonas. L. Schieferstein, C. Kriiger, and Y.-H. Tsay, Angew. Chem. Int. Ed. Engl., 18. 550 (1979); (b) A. Carbonaro. A. Greco. and G. Dall'asta, J. Organomet. Chem.,20, 177-186 (1969). K. Jonas. Adv. Organomet. Qiem., 19.97 (1981). P.-T. Chew, C. D. Cook, S. C. Nyburg, and K. Y. Wan, Inorg. a m . , 10.2210 (1971). (a) E. Uhlig and D. Walther, Coord. Qiem. Rev., S, 3 (1980); (b) Reference 17, p. 465. (a) K. Kitaura, S. Sakati, and K. Morokurna, Inorg. Qiem.,20. 2292 (1981); (b) K. Jonas and C. Kriiger, Azlgew. Chem. I d . Ed. .&gL., 19, 520 (1980); (c) T. H. Upton and W. A. Goddard III, J. Am. Chem. Soc., 100.321 (1978). (a) P.-T. Cheng. C. D. Cook. C. H. Koo, S. C. Nyburg, and M. T. Shiomi, Acta Crystallogr., Sect. B, 27, 1909 (1971); (b) W. Dreissig and H. Dietrich, Acta O y s t a l l o g r . , Sect. B, 24, 108 (1968). (a) L. Pauling, "The Nature of the Chemical Bond", Cornell University Press, Ithaca, New York, 1960, Third Edition; (b) G. W. Wheland, "Resonance in Organic Chemistry", Wiley & Sons, New York, 1955; (c) C. A. Russell, "The &story of Valence", Leichester University Press, Leichester, United Kingdom. 1971. Calculations perfo,.med using the method reported by A. F.Voter and W. A. Goddard 111, Chem. P h y s . , 57.253 (1981). (a) H. 0.House, "Modern Synthetic Reactions",.'!I A. Benjamin Co., Menlo Park, California, 1972, Second Edition, pp. 520-530; (b) J. March, "Advanced Organic Chemistry: Reactions, Mechanisms and Structure". McGraw-Hill. New York, 1968, Chapter 2. Reference 26(b), Chapter 8, especially 58.2. (a) C. J. Balhausen, "Introduction to Ligand Field Theory". McGrawHill, New York, 1962; (b) C. E. Moore, "Atomic Energy Levels", National Bureau of Standards Reference Data Series, NBS 35, U. S. Government Printing Office, Washington, DC, 1971. Reference l(e), p. 109. (a) M . J. Doyle, M. Mcbieeking, and P. Binger, J. Am. them. Soc., Chem. Commun., 376 (1976); (b) P. Binger, M. J. Doyle. J. McMeeking, C. Kriiger, and Y.-H. Tsay, J. Organomet. them., 1'35, 405 (1977); (c) P. Binger and M. J . Doyle, ibid.,162, 195 (1978); (d) R. J. DePasquale, ibid.,32, J. (hem. Soc., Dalton Trans.,2491 (1973. (33) J. Ashley-Smith, M. Green, and F. G. A. Stone, J. Chem. Soc. (A), 3019 (1969). (34) Reference 9, p. 106. (35) C. F. Fischer, 'The Hartree-Fock Method for Atoms", Wiley & Sons, Kew York, 1977. (36) (a) K. Clauss and H. Bestian, Justus Liebigs Ann. Chern., 634. 8 (1962); (b) H. Sinn and W. Kaminsky, Adv. Grgammt. Chem., 18.99 (1980). (37) (a) Y. Wakatsuki, T. Kiramitsu, and H.Yamazaki, Tetrahedron Lett., 4549 (1974); (b) J. P. Collman, Acc. atem. Res.. 1. 136 (1968); (c) P. W. Jolly and G. Wilke, "The Organic Chemistry of Nickel", Academic Press, New York, 1974, Vol. 11, Chapter II; (d) H. Suzuki, K. Itoh, Y. Ishi, K. Simon, and J. A. Ibers, J. Am. (;hem. Soc., 98,8994 (1976). (38) (a) Reference l(e), p. 108; (b) J. L. Thomas, Inorg. Qtem., 17. 1507 (1978); (c) J. L. Thomas, J. Am. Chem. Soc., 95, 1838 (1973); (d) H. Hoberg, D. Schaefer, &d G. Burkhardt, J. Organornet. Chem., 228. C21 (1982); (e) M. Kadonaga, N. Yasuoka, and N. Kasai, J. Chem. Soc., Chem. Commun., 1597 (1971); (f) R. J. DePasquale, J. Orgummet. Chem., 32,381 (1971). (39) The Ti basis set is from A. K. Rappe', T. A. Smedley, and W. A. Goddard 111, J . Phys. Chem.. &. 2607 (1981). The carbon and hydrogen (scaled, double zeta) basis sets can be found in T. H. Dunning, Jr., and P. J. Hay, in "Modern Theoretical Chemistry: Methods of Electronic Structure Theory", H. F. Schaefer, 111, Ed., Plenum Press, Kew York, 1977, Vol. 3, and references therein. (a) W. A. Goddard III and A. K. Rappe', in "Potential Energy Surfaces and Dynamics Calculations". D. G. Truhlar. Ed., Plenum Press. New York, 1981, pp. 661-684; (b) A. K. Rappe', T. A. Smedley, and W. A. Goddard Ill, J. Phys. Chem., 85,1662 (1981). P. C. Wailes, R. S. P. Coutts, and H. Weingold, "Organometallic Chemistry of Titanium, Zirconium, and Hafnium". Academic Press, Kew York. 1974. Chapter Ill. This is the overlap of the two GVB orbitals describing the H-H bond in He. Geometry of this species taken from "Landolt-Bornstein Numerical Data and Functional Relationships in Science and Technology. Group 11, Volume 7, Structure Data of Free Polyatomic Molecules", K.-H. Hellwege, Ed., Springer Verlag, Berlin, 1976. For these model calculations we kept the C12Ti fragment frozen, assigned r(Ti-H) = 1.70 (ref 12). r(Ti-C) = 2.02 ;i (ref lo), and e(C-Ti-H) = 75" (ref 10;. r(Ti-C1) = 2.328 and *(Cl-Ti-Cl) = 140". The geometry of this diatomic was taken from K. P. Huber and G. Herzberg, "Molecular Spectra and Molecular Structure. TV. Constants of Diatomic Molecules", Van Nostrand Reinhold Co.. New D York, 1979. The value r(Cr-H) = 1.655 A was used. See also S. P. Walch and C. W. Bauschlicher, Jr., J. men. Phys., 78,4597 (1983). M. L. Steigerwald and W. A. Goddard In, Orgammetallics, t o be submitted. Chapter 4. Reactions of 4with ClzZrH I. Introduction In the first paper of this series' (Paper I), we showed t h a t suprafacial 2 + 2 reactions such as 1 M-H M H D-D D D 0 . e (1) L are allo-<red (i.e., proceed s i t h low activation barriers) if the hi-E-I bond of the reactant "hydride" is a covalent (nonpolar) bond between the two cei.,i?:s and if rhis bond involves mostly d orbital character on !*I L-e c o n p e r e d three reactions (1. Fv: = C12TlC. CIZTi, and ci23c) of hpdrides of trhrisition n e i a l s of the first series and showed t h a t the activation barrier for these alloxed. reactions varied in an understandable Kay. In the s e c o n l pa2er of t h e s e r i e ~we , ~ presented the main-group couriterpoint, inc!icating t h a t in one cese (reaction 1. 31 = H ~ B : valence p orbital: on Iil c o - ~ l dafTord sufficient stability to t h e l::i, transition state t o 8110-$<t h e norpolar 2, + 2, reaction to occur but t h a t , in keneral, polar transition sta:es fire found in these reactions t h a t cannot take advantage of vaience d o r b ~ i a l sor. V In this report we extend our studies to transition rneials oi the second zsries and show- that in the case of zirconium (reaction 1. L: = ClzZr) the reaction is again alloxed, that it proceeds through a nonpolar trar.s~:ion s t a t e , and t h a t t h e difference in activation barrier bziviztln s t r i c t ! analogoiis titanium- and zirconium-centered reaciions can be r e i i t t d to f,lndi.men!.i.! diEsrences betviceri the titanium aiid zircsriiilm We have calculated the activation barrier for the reaction of Cl2ZrH with D2 (reaction 1, M = CIzZr). These calculations were based on the generalized valence bond (GVB) technique? using the method described in Paper I. The geometries of ClzZrH and the transition state ClpZr(H)(D)z were optimized, and the optimum geometries are reported in Tables I and 11. Included for comparison are the geometries optimized previously for CIzTiH and C4R(H)(D);!(reaction 1. M = ClzTi). The reaction at zirconium is 4.3 kcal/mol lower in energy than the reaction a t titanium. In Table I11 we list activation barriers and Mulliken population data for the two reactions. These data show that the two reactions are similar not only in their low activation energies but also in the nonpolarity of their transition states. Thus, in general terms, zirconium responds just as scandium and titanium: the 2, + 2, reaction is a "direct hydrogen transier""~ opposed to the "hydride transfer", which is characteristic of the alkali metal hydrides.2 In Figure 1 we show plots of the four one- electron GVB orbitalsS5 which are active in the ClzZrH + D2 reaction. Just as in the case of C12TiH' + D2, the active orbitals here are seen to delocalize to form two three-center, two-electron bonds in the transition state. Bond 1 starts the reaction as the D-D bond, becomes the H . , , D . . . D three-center bond a t the transition state and completes the reaction as the new H-D bond. Bond 2 starts the reaction as the Zr-H bond, delocalizes to from the unspieget H . . Zr , . . T) three-center bond at the transition state and subsequently relocalizes to form the new Zr-D bond in the product. For comparison we show the corresponding set of active orbitals for the QTiH + De reaction in Figure 2. This corroborates the conceptual s i v j l a r ity of the tvio reactions There is a fifth "pseudo-active" electron in each of these two reactions since ClZT1H and ClzZrH (and the related transition states) a r e radicals. In each case this unpaired electron is in an orbital t h a t m u s t remain orthogonal t o the bonds t h a t are in motior~during t h e resciion. In Figure 3 vie display the orbitals that contain the unpaired electron in the reactants and transiticn s:ates for each reaction. In Tabie v;e sk~ow h o the ~ energies of these orbitals change during the reaction. The plots iii Fizure S shoiv that the singiy-occupied orbita! in both C12Zr% an6 CiiTiii is in the piane of the four-cer.ter reaction. Since the orthogonaiization of this orbital to ih* orbitals of the reaction is no: obriated by syrr,rr,etrj-, i t is possible t h a t it ~3.11raise the activation barrier for the pericyclic reac.. 'LICE In order LO understand the diiference in activation barriers between the ~vcoreactions, u-e have studied ClzZrHzand c~,TIH~.? In Tabit. 1- we compare t h e optimum geometries for t h e two molecules and include lidliken population data that indicate the M-H bonds Ere not significzntly polar tov;ard hydrogen in either case. The fact t h a t these U-H bonds should n o t be viexed as hydridice is higlllighted by the orbita! descriptions of these bonds, vchich a r e given in Figures 4 and 5. 111. Discussion The outstanding difference between the titanium and zirconium atoms is that the valence s and valence d orbitals are closer in size in zirconium than in titaniume (Figure 6). This is simply due t o the requirement that the 4d orbitals in zirconium be orthogonal to the ci-xfc! shsli of 3d o r b i t a ! ~ vihile , the 3d orbitals of titanium have no such core orbi:a!s to avoid Tius orthogonality requirement iorces the incorporation of 6 radial node in the 4d orbitals of zirconium, resulting in their increesed size Since ihis requirement applies to the valence d orbitals 0:' atoms ir, both t h e second and third transition series, d orbitals in atoms of the f r s t series may be thought of as being mdersized i n the same vcay t i s t the valence p orbitals are undersized in atoms of the first (rriain group) rori oi the periodic table.'.1° Since there is such a disparity in rzle!ive sizes, the energy of the 4s orbital on titanium is quite high (3.1 e\.)" z;ls- a- th- 3d orbitals, while in zirconium the energies of ths .5iend 4c! orbitals are close by comparison (1.8 e 1 3 . l ~ In Table 17 we report s and d ionization potentials for the two atoms, sho-wing the 70 kcal/mcl energetic separation of 3d and 4s in titanium and the 40 kcal/mol se2aration oi 46 and 5: in zirconium. In cases such as tilitnium, in which there a r e two atomic orbitals in the valence region of an atom that are of markedly diflerent energy, the more electronegative "one-electron" ligands %-ill use the orbital t h a t is the higher in energy of the two, leaving the h e r energy orbiia! to 52 used by the less electronegative Iigands. This effect can be traced t o the polarity of the hi-X bond. The greater the electronegativity of X, the more irnpor:ant the X'X- component is in the description of the bond. Tfur ionic component will b e lower in energy when the orbital on M, M-hichis ionized, is lovier in energy. Thus, the greater electronegativity of X will result in the greater tendency of X t o bond t o the more easily ionized orbital.loa Thus, in CIZTtH2, the chlorine Iigmds bond preferentially t o the 4s orbital ontitanium, while the hydrogen atoms bond t o the 3d orbital: that rernain. This is to be distinguished from the case ~f CliZrE;! in chlch there is less discrepancy in the natures of the Zr-C1 and Zr-H b3nd-r. Hcnce, while the titanium-centered orbital of the Ti-H bond in C1zTiX2 is 74% Ti-d, the corresponding zirconium orbital in ClZZrNZis only 58% Zr-dl2 (in each cese t h e remainder o! the orbital i~ metallic ~ a l e n c es an? 2 in character). Stated in other terms, the energetic closeness of the zirconium 51 and -Id orbitds allavis s / d hybridization t c occur more frs$ly (in Pau!ing's terms, the promotion energy is smaller 13\1 . One result of this free mixing is the larger H-hi-H angle in ClzZrH2 than in Cl2T~HZ.T h s may be rationalized by noting that simplest valence bond idess predict t h a t the angle between tv-o covalent u bonds to two d orbitals on the same metal \c-il! be 54.74' (or 125.26")'.'' (ignoring steric ef;ec?s and electron correintion). Similarly, the angle betvieen t x o o bonds t o two slplhybrid orbitals in the same metal is predicted to be l i 3 0 ' . ' ~ ~In the limit of no sp-d hybridization (and i~noririgsieric and correlation effects), the CI-hi-Cl angle in C1~31.H~(M = Ti, Zr) is thus predicted t o be 180" and the H-M-Hartgle 54.74' (or 125.25'). I n c r e ~ s e d sp-d hybridization will lead t o four bonds that are more equivzlent and a concorni:arii tendency of the bond angles toward the tetrahedral averhie. The energetic disparity between valence s and valence d also has an effect on the electronic structure of C12X:H. The metal-centered orbital in the TI-H bond in ClZTlH is 65% d, while the corresponding orbital in the zirconium case is only 52% d." lnlerestingly, the singly-occupied orbital in CIZTIH is 94% d, while t h e zirconium-centered singly-occupied orbital is only 74% d T h s further evinces the ease of s-p-d hybridizaiion in Zr and the energetic difiiculty of this in the case of Ti. In Paper I N-e asserted t h a t the 2, + 2, reaction, 1, would be lower in energy for the hl-H bonds, which are more d-like on the metal. Here vze present a case that violates that prescription. The reaction a t CliZrH is lower in energy than the reaction a ? CI2TlH, even though the Zr-H bond has less d character than the Ti-H bond (Table I). The simple rule postulated in Paper I m u s t be amended to account for tne iact that a n atom such as zirconium is able t o form strong bonds with its valence d orbitals as %ell as ~ j i t hits valence s and p orbitals. In the discussion ia Paper I , it was assumed t h a t t h e removal of metallic s and p components of the 5;-H bond when the G-H3 bond wzs formed would be energeticaliy quite ccs?!?. This was due to our belief t h a t "d" bonds a r e intrinsically weaker than "s" bonis. This appears to be no; so much the case ~ 5 t htransition m e t d s of the second row, OM-ingt o t h e similarity in radial extent of the s and d orbitals. In t h e case of titanium, the overlap of the atomic 4s orbital with a 1s orbital on a hydrogen atom 1.7 l5 aviay is 0.444, and t h e overlap of s n atomic 3dz2 orbital with that. same hydrogen 1s orbital is 0 1 9 9 l6 In the case of zirconium, the overlap of the atomic 5s orbital with the 1s orbital on a hydrogen atom is 1.87 " away is 0.402, while that of the atomic 4di, is 0.304. Thus, the zirconium valence d orbitals are expected t o bond t o "one-electron iigands" a s effectively as thi: valence s . le In Paper 11, we proposed t h a t the barrier for reaction 1 depended on the abillty of M to form an "unspiegelu6 bond with the Hg radical. Tbs bond is drawn schematically in (2). In this structure, the two fragments of the transition s t a t e (M and HJ)are held together by a bond between the antisymmetric (unspiegel) oneelectron orbital on hi and the delocalized and antisymmetric (unspiegel) orbital on H3. Thus we shoived t h a t the activation barrier for reaction 1 could be dissected into its components, one of which is the ability of the unspif.ge1 orbital on L I to form strong li bonds. Comparison of Figures 1 and 2 and the overlaps in Tables I and 111 bespeaks the greater ability of zirconium t h a n titanium t o form such r; bonds. This is becaurz the antisymmetric (unspiegel) zirconium 4d orbital t h a t mediates the h:-Hz b o d L. larger (ia proportion) than the correspondirg o:".i:al CI,Ti:H):D), 5: in This provides for greater overlap of the two orbitals of the . D bond in the zirconiun; reaction than in the t i t a n i m re&:- tion, and this in t u r n leads t o a lcwer activation barrier. In this way, even though more s and p character is quenched from the Zr-H bond a? the C12Zr[H)(D)2 transition s t a t e , t h e comparable strengths of the Zr "s" and "d" bonds makes the activation barrier for the zirconium-ixediatzd 2, + Zz reaction lower. The unpaired electron on M (Table n' and Figure 3) has less eflzct on reaction 1 for M = Ci2Zr than for I+! = ClzTi, a s evidenced by the changes in orbital energies Apparently, in neither case is the orthogonaiization of this orbital t o t h e incoming 4 unit energetically prohibitive N. Conclusion In this paper we have shown that 1) the suprafacial 2 + 2 reaction between C12ZrH and De is allowed and proceeds with an activation barrier lower than that for the corresponding reaction a t C1,TiH; 2) this lower activation barrier is due to the greater ability of C12Zr than C12Ti to form an unspiegel "n-bond" with I-Is; and 3) this ability is due to the greater radial extent of the Zr (4d) orbital than the Ti (3d) orbital. We have also shown that the s-to-d rehybridization about zirconium, whch is necessary for the process of the 2, + 2, reaction is low in energy because the valence s and d orbitals on Zr are close in size,g energy,11 and in their ability to overlap the bonding orbitals of a one-electron ligand such as H . We have also shown that the Zr-H bond in CIZZrHis quite similar to the Zr-H bond in CI2ZrH2, and that the singly-occupied orbital on zirconium in C12ZrH is not severely affected during the 2, + 2, reaction. Given these data, we suggest that these results [reactions of CIzZrH, an example of "organometallic" Zr(II1); can be used in the analysis of the reactions of the "organometallic" reactions of Zr(N) complexes.'g Reactions of Zr(N) complexes with HZ (D2) have been observed by Bercaw [(3lZ0and (4)"] and Schwartz [(5)22]. r + H, Cp2 z r ~ CpzZrH2 + 6 (5) Mechanisms have been proposed for these reactions that invoke either migration of H(D) to the cyclopentadienyl ring2' or dipolar (heterolytic) cleavage of Hz (D,)." Our results indicate that while such mechanisms may occur, there is a simpler, direct route available to such complexes. The direct hydrogenolysis of such Zr-R bonds (R = H, D, alkyl) has been ' ~e concur and cite these reactions as suggested by ~ r i n t z i n ~ e r . W several of the same class of pericyciic 2, + 2, reaction. Results shown in Figure 1 and Table I1 indicate that these reactions should not be viewed as heterolytic or even polar, but as nonpolar and pericyclic. Based on the topological similarity of the H-Hbond in Hzt o the C-C n bond in simple ole fin^,'^ we can also extend our results to the analysis of reactions such as (6:' We claim that these hydrozirconation reactions can also proceed via a very simple pericyclic niechanism involving the four-center intermediate Finally, we believe that these results can be extended to the description of the reaction shown in ( o ) ~ ' in Paper 111 of this series,25 we described the electronic structure of r C1,Ti-CH2-CH,, indicating the strain in the metaUacycloprop&ne ring. We claimed that the reaction shown in (9)26 should be viewed as a ring-expanding migratory insertion reaction that is pldshed by this strain. We suggest that the same mechanism is operative in the zirconium case (8). Owng to the greater radial extent of the valence d orbitals on zirconium, the ethylene complex of Cp,*Zr is even more likely to be a metallacyclopropane than is the ethylene complex of Cp2 'Ti. Apprndix: Details of the Calculations These calculations were performed a t the fully a b initio All electrons were included in the calculations save the t e n core electrons on each chlorine. These electrons were replaced by an ab initio effective potentid.2e The valence e l e c i r o n on chlorine were described by a minimal basis s e t that was optimized for molecular environment^.^^ T h s bzsis emphasizes the chloride character of these ligands. The metals were described by valence double zeta basis sets,30 and the hydrogen atoms by a triple zeta set.31 Tn? geometries of the two titanium species involved in t h e 2 i2 reaction were described in Paper I. The geometry of the C1,ZrHz molecule was opt-zed in a point-by-point fashion using G14(2/4) v;avefunctions in which the two Zr-I1 bonds were described by 73 pzirs of GT-3 orbit~!s.-- The geometry of C1,ZrH was optimized at the Gl73(1/2) keeping the CIZZr fragment fixed a t t h a t of the C12ZrHz m3lecuie. Tfie geometry of the C12Zr[H):D)2 molecuie %-asoptimized a t the HF level in s point-by-point way. The height of the activation barrier for the 2, + 2, reaction (AE in Table 111) %-asdetermined by the method described in Paper I . in Table 'Ill vte report the final total energies for the species pertinent to reaction 1. - Table I. Geometries of C&MH.a , b Molecule r (M- C1) r (M-H) i) 1.901 C&ZrH (2,450 ChTiH (2.328 A) 1.70 A O(C1-M-C1) Mulliken Populations in M-H Bond Pair M M H (valence (valence dl and I (127.2") 0.55 0.43 1.03 (140") 0.70 0.37 0.87 a Values in parentheses were fixed at those from ChMH,. Other parameters were optimized using a GVB(l/2) wavefunction. Both molecules were found to be planar. Table a. Geometries of C4M _rm_ Molecule l-I \ D/ rz 6 a The geometry of the C4M fragment was fixed at that of the C P I + molecule. CZVsymmetry was assumed for both complexes. a Mulliken Populations M Transition State D.-OM**-H Bond AE Total on hydrogen in MH, terminal central (kcal/mol) s P d Zr 17.4 0.0 0.12 0.60 1.02 n 21.7 0.0 0.11 0.72 0. 93 - GVB Pair Overlaps SYm antisym 0.86 0.85 0.80 0.82 0.84 0.70 Table IV. Orbital Energies of Singly-Occupied ~ r b i t a l s . ~ mYm_ Molecule Orbital Energy of Singly-Occupied Orbital (hartree) a A l l values are results of GVB(1/2) or GVB(2/4) calculations. M Geometry r(M-H) a Reference 31. r(M-Cl) 8 (Ci-M-C1) 8(H-M-H) Table VI. Ionization Potentials of Z r and Ti Atoms. a, b _n__U Ionization a Quantities averaged over J states. From ref 11. Energy - A(= "d" ~p "s" 1p) Table M. Total Energies. _VmM A. C4MH Total Energy (hartree) GVB(1/2) GVB(1/2)-RCI * excitations single Figure 1. G\B orbitals active in the reaction of ClzZrH with 4. (i) Reac- tants. (ii: Transition state. (iii) Products. The separation between adjacent contours is 0 05 a u., and the dimension of each plot is 6 a.u. figure 2. GVB orbitals active in the reaction of ClZTiH with DZ. (i) Reac- . tants. (ii) Transition state. (iii) Products, The separation between adjacent contours is 0.05 a.u., and the dimension of each plot is 6 a.u. Figure 3. Plots of the singly-occupied orbitals in C12ZrH, C12ZrH3, C12TiH, and CIZTtHs. The separation between adjacent contours is 0.05 a.u., and the dimension of each plok is 6 a.u. Singly -Occupied Orbitals Ti, Figure 4. GI% orbitals describing the Zr-H bonds in ClZZrH2 The separa- tion between adjacent contours is 0.05 a.u., and the dimension of each plot is 6 a.u Zr-H bonds in C12Zr H2 Figure 5. GI73 orbitals describing the Ti-H bonds in CIZTIHZ. The separation between adjacent contours is 0.05 a.u.. and the dimension of each plot is 6 a.u. Ti - H bonds in CI2TiH2 Titanium and Zirconium Atomic Orbitals Figure 6. Valence s and d,r orbitals Ior the zirconium and titanium atoms. The separation between adjacent contours is 0.05 a.u., and the dimension of each plot is 6 a.u. References and Notes (1) hl. L. Steigerwald and W. A. Goddard 111, (Paper I) J. A m . C h e m . Soc., in press. (2) hl. L. Steigerffald and 'H'. A. Goddard 111, J. A m . & e m . Soc., t o b e submitted. (3) 12'. A Goddard Ill, T. H. Dunning. Jr., W. J . Hunt, and P . J . Hay. Acc. C h e m Res., 6, 368 (1973). (4) (a) P. J. Brothers. B o g . Inorg. Chem., 2, 1-67 (1981); (b) H. H. J Brintzinger. J. Organornet. &ern., 171, 337-344 (1979,. (5) Recall in GVB t h a t bonds are formed from o ~ e r l a p p i n g ,singlyoccupied orbitals; ref 3; also TI'. A: Goddard 111, J. A m . Chem. Soc.. 94. 793-807 (1972). (6) In Paper 11 (ref 2), we defined an orbital o r bonding pair of orbitals t o be spiegel if they were symmetric under reflection in a given plane and unspiegel if antisymmetric. These t e r m s are the generalization of sigma and pi, respec:ively. (7) A . K. Rappe' and TS. A. Goddard 111, J. A m . C h e m . Soc., 104, 297-299 (1982;. (8) Examples of hydridic species a r e shown i n ref 2 (9) C. F. Fischer, "The Hartree-Fock Method for Atoms", Wiley ti Sons, New York, 1977. (10) K. A . Goddard III and L. B. Harding, Ann. R e v . P h y s Chem., 29, 363-396 (1 978). (1 1) C. E. Moore. "Atomic Energy Levels". NBS Ref. Data Series, NBS 35, U.S. Government Printing Office. Washington, DC, 1971. These hybridizations are based on relative Mulliken populations of d and s + p functions on the metal. L. Pauiing, "The h'ature of the Chemical Bond", Third Edition. Cornell University Press, Ithaca, Kew York, 1960; 64.5. (a) Reference 13, p. 152; (b) J. W. Lauher and R. Hoffmann, J. Am. Chem. Soc., 98, 1729-1742 (1976). Tle value of R(Ti-H) of 1.70 is found for both C~ZTIHZ(ref 7: t?nd CIZTiH (ref 1). I These overlaps are of atomic orbitals, i.e., not self-consistently optimized. The atomic orbitals came from HF calculations on the appropriate (s2d" state of the Zr and Ti atoms, and a similar calculation on the ground state of the hydrogen atom. This value of R(Zr-H) is besed on results shown in Tables I and V. We believe that t h s feature of zirconium, as well as the fact that the u p a i r e d electron in C12ZrH is in an orbital w-hich, in comparison to the corresponding orbital in Cl2T1H, has such a large component of valence s character, accounts for the dearth of examples of o~ganometalliccomplexes of zirconium(II1); see Ref. 19. P. C. K'ailes, R. S. P. Coutts, and H. Weingold. "Organometallic Chemistry of Titanium, Zirconium, and Hafnium", Academic Press, Kev York. 1974. J. E. Bercan, "Transition Metal Hydrides", Advances in Chemistry Series of the American Chemical Society, 1978, pp. 136-148. D. R. McAlister, D. K. Erwin, and J . E. Bercaw, J. Am. Chem. Soc.. 100,5966-5968 (1978). (22) K. I. Gel1 and J . Schviartz, J. .dm. Chem. Soc., 100,3256 (1978). (23) This refers to the similarity of the two bonds when they are involved in a 2, + 2;type reaction; see ref 2. (24) J. Schwartz and J. A. Labinger, Angew. Chem. Int. Ed. Engl., 15. 333-340 (1976). (25) M. L. Steigerviald and R. A. Goddard 111, (Paper 111). J. Am. Chem. Soc., t o be submitted. (26: S. A . Cohen, P. R. Auburn, and J . E. Bercaw, J. Am. Chem. S o c . , 105, 1136-1143 (1983). (27) R . A. Bair, M'. A.Goddard 111, A. F. Voter, A. K. Rappe'. L. G. Yaffe. F. M-. ijobrowicz, I<-.R. Radt, P. J. Hay, and 8.J. Hunt, GVB2P5 Program, unpublished. See R. A . Bair, Ph.D. Thesis, California Institute of Technology (1980); F. R. B o b r o ~ i c zand IY. A. Goddard 111, "hlethods in Theoretical Chemistry", H. F. Schaefer, Ed.. Plenum Press, X'ev; York, 1979; Vol. 3, p. 77; iY. J. Hunt, P.J . Hay, and V;. A . Goddard 111, J. Chem. Phys., 57. 738 (1972). (28) A K. Rappe', T. A . Smedley, and W. A.Goddard 111, J. Phys. Chem., 85, 1662 (1981). (29: IT. A . Goddard I1 and A. K. Rappe', in "Potential Energy Surfaces and Dynamics Calculations", D. G. Truhlar, Ed., Plenum Press. Sew York, 1981, pp. 661-684. (30) A . K Rappe', T. A. Smedley, and tY. A . Goddard 111, J. Phys. Chem., 8s.2607 (1981). (31) T, H. Dunning, J r . , and P. J. Hay, in "Modern Theoretical chemistry: Methods of Electronic Structure Theory", H. F. Schaefer 111, Ed., Plenum Press, New York, 1977, Vol. 3 and references therein. (32) The HZrH angle was optimized a t t h e HF, G\;B(2/4), and GVB(2/4)- RCI levels. The optimum angles were found t o be 104.8", 103.0", and 102.1°, respsctively. A t the GL73(2/4)-RC1 level, t h e difference in energy for 13 = 105" and 13 = 75" is 2.2 kcal/mol, and a t the HF level, this difference is 3.1 kcal/mol. For CIZTiH2, the energy difference betw-een 13(HTiH) = 75" and t? = 105" is 3.2 kcal/mol ( a t the HF level). (33) For Cl2T1H, G\.'B(1/2), acd GLB(l/Z)-RCI calculations gave the same This leads us to befleve t h a t the TI-H bond length t o within 0.004 i. GVB(l/Z) level sufficiently accounts for the Zr-H bond length optimization in C12ZrH. Chapter 5. The Effect of IIybridization on Reactions at Transition Metals. 1, lfybridixation of Atomic Orbitals on Transition Metals In the preceding chapters we have shown that suprafacial 2 + 2 reac- tions at transition metals can occur with low activation barriers. Ke have also shown two examples in which the 2. + 2, reaction does not proceed a t low energy. even though transition metals are involved. We showed graphically that the trend in transition metal 2, + 2, reactibliy is related to the ability of the metal to use its valence d orbitals during the concerted reaction. Ke no&-turn to the direct study of hox- atomic s. p, and d orbitcrls on transiiion metals mix to form hybrid orbitals that are the i optimum orbitals for bonding in the reactants, transition states, and products of reactions. The k o a l is to appreciate the eEects that dictate hybridization in transition metal covalent bonding and how demanding these e3ects are. In particular, it is important to understand the energetics of ( 1 ) . e f / spd hybrid f + X-Yd orbital .............. y m a t is the cost ol the rehybridization that allows the 2, t 2, reaction to take place? Y;e have found simple valence bond ideas1 and calculations quite usefu! in these studies. Recall simple valence bond claims that bonds are formed by the overlap of simpie atomic orbitals--there is no selfconsistent optimization of the sizes and shapes of the bonding orbitals. The simp!e valence bond description of (2) indicates t h a t where 5 = overlap of orbitals p~ and q B = <;sA ;sB> / and H,,= <,; H ?,> It hes been claimed t h & t changes in overall electronic kinetic energy dominate chemical bonding (see Appendix]. 3 For process (21, the change in total electronic kinetic energy is given by where and T,, = <p,iT.p,> , T = kinet~cenergy operator . In this study we czlculate A& a s a function of the spd hybridization of the metal orbital for process (2) in which cp, is a transition metal-centered orbital and cp, is either a hydrogen o r carbon orbital. The use of simple 182 valence bond wavefunctions allows the effect of hybridization to be tested directly; and the &T parameter is a useful one because it is a one- electron quantity and is thus easily calculated. The results of this work indicate that, considering the exchange kinetic energy (LET) along, the optimum mixture of valence s/valence p valence d in transition metalhydrogen and -carbon bonds is 40% (s and p)/60% d; and that the discrimination in use between valence s and valence p, in the spd hybridization is not strong 11. Shapes of Lhe Hybrid Orbitals An spd hybrid orbital may be defined a s in (5), in which v, is t h e metal valence s orbital, y,, is the metal valence p, orbital, and pdtZ is t h e metal-valence dZeorbital.' In the present work v;e used y p . ppz. and ;dE, for the metals that came from self-consistent field (Hartree-Fock) calculations on the appropriate atomic s t a t e s Thus, for a / particular metal and a particular parameter s e t (as, n, a d ) , the hybrid orbital Is c~mp1e:ely specified. In figure 1 we show ,,; ypl, and yd for titanium. The s and d orbitals IE are taken from t h e 4;i'3d2 s t a t e and the p orbital from the 4s'&p'3d2s t a t e of the atom. In Figure 2 we show five orbitals t h a t are linear combination of y , and ?dl, ( p k y b n d , a, = 0, a, and ad varied, a, + ad = 1). In Figure 3 we show yhgbnd (again for Ti) with a,/ a, I 1.17,5 varying the ( a , + a,) / a d ratio. In Figure 4 we show a t h r d s e t of titanium hybrid orbitals, those with ( a , + a p ) / a dset a t 4 / 6 , with t h e a./a, ratio In Figures 5, 6 , and 7 , we shov hybrid orbitals for zirconium, manganese, and nickel, all with a, = 0 and a v a r y i n ~&,/ad ratio. 7 These orbital plots show what spd hybrid orbitals on transition metals look like. They s h o r t h a t even though t h e s and p orbitals are significantly more diffuse than the valence d orbitals, t h e s p hybridization is quite effective ir, changing t h e shape of the d orbital. The M u -zeness of the s and p orbitals is apparent not only f r o m Figure 1 but also from t h e f a c t that t h e spd hybrids look so much like the p w e n t d orbita! until ( a , + a P ) / a d is large. The effects of hybridizaticn a r e clear: adding s character to the d orbital diminishes t h e "doughnut" of the d orbital, and addition or p character "points" the sd hybrid t o one side or the other. 111. Bonding t o Ilybrid Orbitals We assessed the importance of hybridization t o chemical bonding in a direct way. We prepared simple valence bond between a hybrid orbital on t h e metal and an atomic Is orbital on a hydrogen atom located a t a bonding distance drom the metal. We calculated the orbital overlap [S in (3) and (4): and the kinetic energy matrix elements, Tij, for this simple valence bond.@ Combination of these quantities gives the exchange kinetic energy, AE:. If we assume t h a t this kinetic energy quantity dominates the chemical bond, then a plot of AE: as a function ofpletal orbital hybridization will indicate what orbital shape is optimum (all else being eqm.1) for bonding to the metal in question. In Figure 8 we plot AET as a function of ( aJ ad) (a, = 0) for Ti-H [r(TiH) = 1.70 &.' This curve indicates t h a t ACT does discriminate on hybridi- zation, and t h a t t h e optimum ratio is (a,/ ad>= 41 /S9. Hence, kinetic energy dictates an optimum sd hybrid t h a t is 60% d . F g u r e 9 shows the corresponding plot of AES versus hybridization for orbitals formed from the Ti valence dz2 orbital and not a 4s orbital, as in Figure 8, but a 4s-4p hybrid that has a,/a, = 1 . 1 7 . ~Here again, the optimum bonding orbital is 57Z d in chiiracter. Although inclusion of this p character does decrease the value of A& by roughly 50% and increase the bonding overlap by 20%,1° it does not alter the amount of d "required" by AE:. In Fig- ure 10 we show the plot of AET versus hybridization for a varying a,/a, ratio, keeping (a, + a , ) / a d = 4/6. This plot shows the comparatively small effect of changes in sp hybridization. In Figure 11 we show how the value of the valence-bond orbital overlap changed with hybridization. It should be noted that s, p, and d contributions are needed t o realize the optimum overlap. The greater directionality of t h e d orbital compensates for its smaller radial extent, making "d bonding" competitive with "s or p bonding". In Figures 12, 13, and 14, we show plots analogous t o Figure 8 for the z~-H." bin-H,12 and N ~ - H 'bonds. ~ In each case t h e optimum value of (adad) is close t o the value of 41/59 observed in Ti-H (37/63 for Zr-H, 45/55 for bln-H, and 43/57 for Ki-H). Oviing t o thls similarity for me:als as varied as Ti, Zr, hfn, and Ki, we conclude t h s t the kiaeiic energy criterion selects a,/ad % 40/'60 for all transition metal hydrides. In Figure 15 we show the valence bond orbital overlaps versus a,/ad / for the Zr-H,&ln-H,and Xi-H bonds. These curves shon the expected variationl%nd indicate the geometrical feasibility of sd hybridization. In f i g u r e 8 we also show A& as a function of ( a d a d ) for the twoE electron valence bond in Ti-C (carbon located 2.02 A from titanium; carbon p, orbital from a Hartree-Fock calculation o n p l a n a ~C H ~ ) . " Here t h e optimum hybridization of the titanium bonding orbital is 44/56--quite close t o t h e value of 41/59 observed in Ti-H. This indicates t h a t the 40160 ratio is persistent in 41-R covalent bonds. In the above discussion, only t h e d,, orbital was considered. In molecular sitautions, it may also be possible to covalently bond t o metal - orbitals shaped like d(s2 f),i.e.. a d orbital having four equivalent lobes. In Figure 8 it is shon t h a t in bonding H(1s: t o Ti(3dz,), AE: = -0.131 hartree ( = 82 kcal/mol). If instead the Ti[3d(z2 - y2); orbital is used, AE: = -0.099 hartree ( = 62 kcal/mol). There is, a t this level of approsimalion, a 20 kcal/mol bias in favor of bonding t o t h e d,, orbital. Since TAA= TBB for PA= 3dz, and VB = 3d;zZ - y'),this difference in A& is due t o differences in Tm and in overlap. The dp orbital has an overlap with the H(1s) orbital of 0.199; the d ( z Z - f ) has an overlap of 0.172. The difference in the off-diagonal kinetic energy matrix element is 10 rnhartree ( = 6.3 kcal/mol). Thus the change in overlap dominates this A(A&), and aq'd,," preference in bonding is expeeted.16 F.The Nature of t h e Chemical Bond The estimation of the chemical bond based on kinetic energy alone is crude but instructive. Pauling advanced t h a t the strength of the chemical bond is proportional t o the square of the valence bond orbital overlap.'? thus postulating t h a t 5 is proportional t o S. Our studies imply 1 +sZ ~ t h a t t h e r e is a monot h a t the relationship is moree c o m p ~ i c a t e d , 'but tonic relationship betn-een S and the bond energy. The kinetic energy studies show t h a t there is a pol\-erful force urging / . t h a t ligands bond covalently t o metallic d orbitals. This force is t h e high kinetic energy t h a t is intrinsic t o the shape of d orbitals." The kinetic energy of an electron in the 3dl,orbital of Ti a t o m is 3.76 h ( = 2360 kcal/mol), while the kinetic energy of an electron in the 4s orbital is only 0.54 h ( = 340 kcal/mol)! The tremendous kinetic energy is decreased v h e n a bond is formed. (3ptimum hybridization gives A& = -0.63 h = -395 kcal/moi for Ti-H.) Based on atomic spectroscopy,20 t h e energy of the Ti (3d) orbital is roughly 3 ei' ( = 69 kcal/mol) Lower than the energy of t h e Ti (4s) orbital. There is therefore a huge difference in the electrostatic potential (oneand two-electron) felt by the 3d and 4s orbitals. Future work will indicate the effect of hybridization on the potential energy terms in the b m d , but a t t h s point we can observe t h a t t h e virial theorem2' indicates t h a t electrons in valence orbitals of complicated atoms do not feel a central force. If they did, t h e diflerence in intrinsic kinetic energies of t h e 4s and 3d orbitals on titanium would be equal to the difference in 4s and 3d ionization potentials This is not t h e case. The kinetic energy analysis suggests t h a t the optimum hybridization of the metal orbital in an M-R covalent bond should be 40% s and p and 60% d. The method of analysis ignores any polar contriibutions to the bond. Bonds that do demonstrate significant polarity will not be described usefully by the described scheme and the 60/40 ratio i s unimportant Bonds that are nonpolar still are observed to have metal-centered hybridization that varies markedly from 6 0 / 4 0 . ~This ~ is due not only to the potential energy terms that were neglected above but also to the presence a t the metaI of more than one ligand and to promotion energy. / In a case such as CIzTiH+ (Chapter I ) , the chIorine Iigands bond preferentialiy to the titanium "4s electrons" (see the discussion in Chapter 4). This means that the valence s and p space on Ti is not available for free use by the nonpolar Ti-H covalent bond. T h s leads to a hybridization in the Ti-H bond with accentuated d character. Pauling defined the term promotion energyz3 in reference to hybridization. Promotion energy is the energy required to prepare the bonding configuration of an atom. Pauling claimed, for example, that the H-H bond in He would be stronger if the 3d orbital on each hydrogen were used rather than the is, but that the energy necessary to prepare the (3d)' state of H atom precluded ths. In the same way, a 60%d/40%smetal orbital may be of the optimum shape for bonding, but if it cost too much to prepare the corresponding state of the atom (as it would in ClMn or Cu; see Chapter 21, the mentioned hybridization would not prevail. V. Conclusion We have studied how the transition metal-to-ligand covalent bond changes with changes in spd hybridization of the metal orbital. We have presented plots of the hybrid orbitals for Ti, Zr, Mn, and Ni, showing pictorially how hybridization effects changes in the shapes of atomic orbitals. We have shown how both the overlap of the metallic orbital with the bonding orbital of a one-electron ligand and the exchange kinetic energy (AE.;)change with changes in metallic orbital hybridization. 'U'e have found that the decrease in electronic kinetic energy r e l i z e d ~ nforming a two-electron chemical bond predicts the optimum hybridization of the metallic orbital of the hi-R bond to be 60% valence d and 40% valence s and valence p. A more practical conclusion of this work is shown in Figure 8. There it is apparent that the hybridization of the metallic orbital of a metalcarbon bond is more flexible than the hybridization of the analogous orbital in a metal-hydrogen bond.Based on the process shown in (1) t h s implies that, all else being equal, a metal-carbon bond is more reactive (in 2 + 2 reactions) than a metal-hydrogen bond. Appendix: Kinetic Energy and the Chemical Bond Perhaps the simplest visualization of the chemical bond relies on the quantum mechanical particle-in-a-box. A particle in a one-dimensional box of infinite energy walls and of dimension a is described by a harniltonian of kinetic energy alone. In the ground state, this particle has an (kinetic) energy of - a1 (arbitrary units). Two such systems taken 2 together have E = - Now consider bringing these two boxes together; az ' i.e., make the separation between the boxes zero and destroy the coincident wall. This gives a single box of characteristic dimension Za,which contains two particles. If the particles are noninteracting, this scenario has a total (kinetic) energy of the two boxes is [ [- 4. Therefore, the "bond energy'' of This is the mathematically simplest realization of the bonding question and is the basis of the molecular orbital model of molecules. Obviously, if the particles interact with one another (e.g., electrostatically), or if there is an external potential (e.g., an electrostatic central field) that is more complicated than the one-dimensional square well, the problem will assume greater complexity, but as it stands, this represents the gross features of the quantum mechanics of the chemical bond. A "valence bond" representation of the bond between two potential "boxes" can be formulated with similar felicity. The results are less immediately obvious but equally simply, varying only slightly from those given in the text of tfus chapter. * In- -- . g g .;;c . P) * -z It 2 . 4 c .O 4 - $ e, 5 m 2 --* -p-.; 2 z ", .a . .-C in m $ &8 - -9: - 5 U m $ 2 % + 2 . 3 2 ; - 0 5 w 2 u d a.e l ; - u = 0 ? X - g O m -2 -Y 0 a ... - m a c J c P) M u 0) 0 " 9 . * $ II 2 $ 3 3; L3 -2 3 3 lor the (a) Ti-H and (b) Ti-C twoFtgure 8. A& as a function of (aJCQ) elecLron valence bond. aJ(a. + ad), Units the abscissa are increments of 0.0 -0.09 - 0.18 AET (hor tree) -0.27 -0.36 - 0.45 40/60 60/40 a , /a; Figure 12. A 4 as a function of (wad) for the two-electron valence bond in Zr-H. Added for reference (upper curve) is the Ti-H curve from Figure 8. References and Notes (1) L. Pauling, "The Kature of the Chemical Bond", Third Edition, Cornell University Press: Ithaca, Kew York, 1960; p. 25. (2) Assume a (valence bond) wavefunction of the form qW = VA+B + IDBFA Then where E(A,B) is the nonquanturn mechanical energy of atom 4 and atom B placed a t a bonding distance. This gives where - t 3 - ( H ~ . B A S2HzB.ne) 25 If H = T,+ T2 (i.e., hamiltonian = sum of kinetic energy operators), then 2S = 'T ~ b n d s 2s'i~ - -Z(TM + TEE)] = l+sZ l + S Z L M (3) ' (a) H. Hellman, 2. Physik, 85. 100 (1933); (b) K. Ruedenberg. Rev. Mod. Phys.. 34. 326 (1962). The term (a: + a; + a$)* insures normalization The ratio of (a./ap) = 1.17 was observed for the self-consistently optimized Ti-H bond in CIZTiH. Since the optimum ratio of sp-hybrid-to-d was found to be 41/59 for the case described by Figure 3, the ratio of (a, + ap)/ad was kept a t 40/60 throughout t h s test. The metal bases used were taken from A. K. Rappea, T. A. Smedley, and W. A . Goddard 111, J. Phys. Chem., 85, 2607 (1981). The hydrogen basis set is a six-gaussian tripie zeta set found in T. H. Dunning, J r . , and P. J. Hay, In "Modern Theoretical Chemistry: Methods of Electronic Structure Theory", H. F. Schaefer, Ed,; Plenum Press: New York. 1977; Vol. 3 and references therein. These caiculations were performed using the LTRtZN program for the Caltech Molecular Quantum Mechanics Program Library. The value of r(Ti-H) = 1.70 was found for the Ti-H bond in C1,TiH (a) (Chapter 1 of this thesis) and in C12TiH2, (b) [ 4 . K. Rappea and W. A. Goddard 111, J. -4m.Chem.Soc., 104, 247 (1982)). For Phybrid pql. = 4*[] = (4Ps + 6rpd)/N, S = 0.412 and AET = -0.406 h. For t 6pd]/N, S = 0.540 and bET = -0.629 h. R(Zr-H) = 1.86 i; see Chapter 4 of t h s thesis 0 R(Mn-H) = 1.7311 A; see K. P. Huber and G. Herzberg, "Molecular Spectra and Molecular Structure. TV. Constants of Diatomic Molecules", Van Nostrand-Reinhold: New York, 1979. (13) R(Ni-H) = 1.475i; see ref. 12 and if <(~,!cPH> = o and <pdjpH> 3 6 then Once o and 6 are calculated, the variation of S with a,/ad is determined. (15) The value of r(Ti-C) is taken from ref 9b (16) This effect has been observed. A. K. Rappe, Ph.D. thesis California Institute of Technology, 1981. (17) Reference 7 , p. 121. (18) Preliminary results of an examination of simple valence bond wavefunctions of HZ at variable internuclear separations indicate that, phenomenologically, the strength of the H-H bond is propor3 tional to the -power of the bonding pair overlap 2 (19) Recall the kinetic energy of a particle in an orbital rp is the (unweighted) average of the gradient of that orbital; hence the more curved the orbital, the higher the kinetic energy of the particle in that orbital. (20) C. E. Moore. "Atomic Energy Levels". NBS Reference Data Series. NBS 35, U. S. Government Printing Office, Washington, DC, 1971. (21) H. Goldstein, "CIassical Mechanics", Addison-Wesley, Reading. Massachusetts, 1950, p . 69. (22) See Chapters 1 , 2. and 4 of t h s thesis. (23) Reference 1, p . 127. Chapter 6. Carbon-Carbon Bond Cleavage in Nickelacyclopentanes I. 2 + ZS Reactions in the Organic chemistry of Nickel s The organic chemistry of nickel1 is dominated by reactions which, at least formally, are suprafacial 2+2 reactions. Oxidative addition, reductive elimination, migratory insertion of coordinated ligands into nickelcarbon bonds and the corresponding de-insertion comprise the set of "normal" reactions of the organometallic complexes of the Group VIII metals. These simple reactions have been cited as the fundamental transformations which govern homogeneous catalysis,2 and have been studied in that light. One of the goals of physical organometallic chemistry must be to gain a detailed understanding of these reactions so that they may be used in a selective way. A) Oxidative Addition Oxidative addition is a standard way to prepare ligand- stabilized alkyl complexes of nickel3 (eq. 1). In the typical case, R1-R2 is an alkyl halide, pseudo-halide or ether,* although oxidative addition of C-H and C-C bonds has been occasionally observed in the nickel triad.' It is also claimed 6 that the oxidative addition of weak carboncarbon n bonds begins the "oxidative-cycloaddition" sequence which has been of use to the synthetic chemist. 7 The mechanics of oxidative addition are understood in a general way, but a detailed physical explanation of the reaction is available only in isolated instances. 8 There are undoubtedly several mechanisms operative in the process, some involving a concerted, three center addition,'' other involving SN2-type displacement of the leaving group in R ~ - R and ~ ,still ~ ~ others involving an intermediate electron-transfer step. l2 The phenomenology is comprehensive in a practical sense: the more electron- rich the metal center, the more facile the addition13 - assuming the peripheral steric and electronic effects are not pathological. Although the oxidative addition reaction is formallx a suprafacial 2+2 reaction, the absence of data precludes the widespread invocation of this intimate electronic mechanism. B) Reductive Elimination If oxidative addition in the step with which catalytic processes at many Group VIII metal sites begin (by introducing the organic substrate to the metal), reductive elimination is the step by which they end.2 Reductive elimination is quite well documented in the chemistry of dialkyl complexes of nickel (eq. 2). This process, also a formal 2s + 2s reaction, also apparently occurs via several distinguishable mechanisms. It has been claimed that simple metal-carbon bond homolysis initiates the sequence in many cases. l4 The incipient radical then "captures" the carbon fragment of the remaining metal-carbon bond, leading to C-C bond formation and the observed alkane. On the other hand, very thorough studies, particularly on palladium dialkyls, imply the existence of a direct, three-center pathway for the elimination.15 As with the oxidative addition reaction, in the case of organometallic complexes of nickel, an extensive empiricad understanding of reductive elimination exists. lt9 Reductive eliminations occur upon thermolysis, oxidation and/or photolysis. In thermal reactions, it has been observed 'that more basic ligands (L in eq. 2) lead to higher barriers to decomposition.l6 This has been rationalized by the citation of the necessary dissociation of one of these donor ligands at the initial stages of the decomposition,15f17 although this has yet to be conclusively demonstrated in the case of nickel dialkyl complexes. Oxidative induction of reductive elimination is well-known. Although the mechanism of the reaction between nickel dialkyls and O2 is not well understood, it is observed that 1 reductive elimination of alkane is the ultimate result. It is quite tempting to suggest the intermediacy of a nickel (111) dialkyl cation, and there is some electrochemical evidence for this.'' Other examples of oxidatively- induced reductive elimination are less obvious. Treatment of stable and isolated dialkyl complexes of nickel with Lewis acids such as AIClj results in the low-temperature elimination of alkane via a mechanistic pathway which is not understood. l9 Treatment of isolated dialkyl complexes of nickel with strongly "n-acidic" olefins such as acylonitrile also results in the low-temperature decomposition of the dialkyl complex,20 this time resulting in activatedolefin complexes of nickel which certainly deserve more attention. The mechanism of this reaction is also not well known, but it has been claimed that the olefin simply oxidizes the dialkyl complex. It is also possible that this reductive elimination is not a simple 2+2 reaction, - but a more complicated six-electron "isovalent" (not reductive) elimination. Photochemically-induced reductive elimination has been observed in rare instances.21 The details of this process are also unknown, but a functional photo-oxidation seems likely. C) Migratory Insertion and De-insertion The migratory insertion reaction pervades the chemistry of nickel. Aside from the oligomerization of olefins and diolefins2* and the coupling of Grignard reagents and aryl halides,23 carbonylation of organic substrates (alkenes, alkynes , organic halides, etc.) 24 is the most useful transformation mediated by organonickel reagents. The heart of this process is the insertion of CO into the nickel-carbon bond-of an intermediate nickel-alkyl complex. Although this step of the catalytic sequence has been modeled extensively, 25 many details of the insertion remain unknown. The simplest electronic interpretation of the insertion is as a suprafacial, three-center 2+2 reaction. The present author believes that a migratory insertion occurs in the zerovalent nickel catalyzed cyclodimerization of activated olefins (eq. 3). The stepwise nature of this coupling has been definitely demonstrated only in the case 26 even of tetrafluoroethylene reacting with (P$3)2Ni(C2H4), though other olefins can be cyclized by this procedure. This is presumably because complexes such as 2 are too reactive to be isolated. " In the case of tetrafluoroethylene, it has been suggested that the ring expansion reaction (4) is a dipolar (nucleophilic) insertion reaction, although this has not been clearly demonstrated. Despite the widespread importance of these nickelmediated migratory insertion reactions, the detailed electronics of the processes are not known. In particular, the structure of the nickel-carbon bond is still the subject of some not unreasonable controvery. In particular, the degree of polarity of the nickel-carbon bond has not been established rmambiguously. Since the ground state of the nickel atom is 3~ (s2 d8 ) two reasonably polar "s bondsn 28 seem likely for the nickel-carbon bonds of nickel dialkyls, but this must be established more rigorously. If these bonds are significantly polar toward carbon, and if they are bonds to the 4s orbitals of the nickel atom, then the migratory insertion reactions at nickel will be of the polar type.29 A detailedstudy of the migratory insertion reaction at the nickel-carbon bond will yield answers to significant questions such as how to best prepare the nickel atom to carry out insertion reactions and how to best prepare the nickel atom to suppress unwanted insertions. One migratory insertion reaction which is only rarely of practical value is the 8-hydrogen transfer reaction. This reaction is crucial to the olefin isomerization reaction of Tolman,30 the Wacker oxidation sequence,31 and the productive 32 activation of saturated hydrocarbons, but in preparative organometallic chemistry, the $-hydrogen reaction is best suppressed. Study of the nickel-based 8-hydrogen reaction has been limited, owing to the paucity of nickel complexes which have @-hydrogens and are nonetheless stable enough to study in the synthetic laboratory,' and decompose at amenable rates via 8-hydrogen transfer pathways. Very elegant studies on bis(phosphine)diethylpalladium complexes have shown that the cis-square planar complex decomposes via reductive elimination, while the trans-square planar complexes decomposes via 0-hydrogen elimination. 33 Although the different reactivity is easily explained on geometrical grounds, it would be of interest to see if other inroads exist for controlling the reactivity of such complexes. Are there other ways to direct the trans complex toward reductive elimination? It is curious that one of the very few diethyl complexes of nickel which is stable is (bpy)NiEt2. This complex thermolyzes to give a mixture of n-butane, ethane and ethylene. 34 A detailed study of this reaction is in order. A final reaction at nickel which is of considerable interest, and is best explained as a ZS + 26 reaction, is the 0-alkyl transfer reaction, 5. Despite the simplicity of this reaction, and its gross similarity to the 8-hydrogen transfer reaction, it has been seen only rarely: (1) Watson has reported that the isobutyl complex 2 will react as in 35 (6). ( 2 ) Equilibrium of the form (7) have been observed or implied for M = * 37 cp22r3' Cp2Ti, and CpC12Ta. 39 (3) Decarbonylation reactions40 have been postulated to proceed through retrograde Zs + 2s reactions. (4) Tris- (triphenylphosphine)nickelacyclopentane decomposes by an apparent 2S + 2s process to give ethylene. 41 This is the only example of simple B-alkyl transfer (or phenomenological equivalent thereof) in the organic chemistry of nickel, and served as the initial point for all of the investigations reported in this thesis. The 0-alkyl transfer reaction is of interest for several reasons: (1) The Ziegler-Natta polymerization of simple 42 olefins occurs via the reverse of the B-alkyl transfer. Conclusions reached concerning the 6-alkyl transfer can easily be inverted to give insight into the polymerization process. ( 2 ) The stereospecificity of the polymerization of propylene remains a mechanistic mystery. 43 1n particular, it is not known whether the Ziegler-Natta systems have the ability to correct their stereochemical mistakes. The most obvious "self-correcting" capacity invokes the removal of the last unit of substituted olefin from the growing polymer chain (a 8-alkyl transfer), stereochemical readjustment, then reinsertion to give the proper polymer chain. Characterization of B-alkyl transfer in independent systems would lend support to this mechanistic twist to the polymerization process. (3) Several studies of the homo- geneous activation of saturated hydrocarbons have been disappointing, because the organometallic complexes resulting from initial insertion into the saturated C-H bond are too stable. 4 4 In other cases, such as that described .by ~rabtree,~'products resulting from 8-hydrogen transfer reactions are too stable. If we knew how to direct 6-alkyl transfer generally, perhaps solutions to these problems in C-H activation could be devised. (4) Reactions which are best rationalized as 8-alkyl transfer reactions have been observed to proceed at naked transition metal cations in the gas phase. 4 5 Studies of active metal complexes in the homogeneous phase could aid in the interpretation of these results. Despite the utility of the 8-alkyl transfer reaction, and owing to its apparent rarity, it has not been extensively studied. I undertook t h e examination of t h e nickel-based r e a c t i o n i n eq. 9 . cis - 4 The q u e s t i o n s of i n t e r e s t were: (1) What i s t h e f o r c e behind t h e c l e a v a g e o f t h e carbon-carbon bond, and ( 2 ) can t h i s f o r c e be c o n t r o l l e d and d i r e c t e d . 11. Previous Work Grubbs and coworkers reported that bis(tripheny1phos- phine)nickelacyclopentane, 4, could be prepared from the corresponding bis(phosphine)nickeldichloride and 1,4dilithiobutane. 41 Based on the available data, it was concluded that this complex is a cis-square planar complex of Ni(I1). When a large excess of phosphine is added to a solution of the metallacyclo in toluene, a new complex results, tris(triphenylphosphine)nickelacyclopentane. 46 When this complex is isolated and excess phosphine removed, a dissociative equilibrium may be observed between 3, free phosphine, and a new complex, 5, which has the stoichiometry, but not the identity of 4 (thus observed by 3 1 NMR). ~ These workers found ethylene to be the major organic product of thennolysis of 3. They suggested that the new complex, 5, is the tetrahedral isomer of the cis square-planar complex 5. The chemistry observed from this set of nickel complexes must be compared to that of the corresponding palladium and platinum complexes. Bis(phenyldimethy1phos- phine)palladacyclopentane is observed to decompose at 70° in toluene to give predominantly 1-butene.47 Bis(tri-nbuty1phosphine)platinacyclopentane decomposes in various solvents to give a variety of products, but the predominating product in all cases is also 1-butene. 48 It should be mentioned that the dominant product of photolysis of eit: :r the nickel (11) or palladium (11) is ethylene. then be able to explain: One must what is the practical difference between Ni, Pd and Pt? The electrbnic difference between nickel, palladium and platinum is immediately apparent. While the ground state of the nickel atom is 3 ~ the , ground state of the palladium atom is '~(4d ) . 49 (For comparison, the 3F state 14d9) in palladium is above the S ' by 3.4 eV, with the 3~(5s between the two, at an energy of 0.9 eV.) In the platinum atom LS coupling is no longer useful, but it is helpful to note that the 3~(6s15d9) state (averaged over L and S) is still the ground state, lying roughly 0.1 eV below the S ' (5d10) and 0.3 eV below the 3~(6s25d8). Thus, the elementary difference between Ni, Pd and Pt is the ground electronic state. The nickel atom adopts the doubly occupied valence-s configuration in its ground state. In this way nickel acts like Be, Mg, Ca, Sr, etc., and is expected to act, in a general way, like a Group IIa metal. In particular, the directed valence associated with a (valence-s)~state predicts a bond angle at the central - atom of 1804. Hence, divalent benyllium, divalent magnesium, divalent calcium, etc., and divalent nickel should show covalent bond angles of 180°. 50 In cases where the geometries of isolated complexes have been determined, this obtains. In fact, in all crystallographic studies of complexes of the form L2NiR2 (L = donor base ligand, R = alkyl ligand; neither L2 nor R2 chelating), the ~ -----o -~ bond ~ angle J g (i.e., ~ ~ the R-Ni-R angle) is 180°. This is to say that all complexes of this form are trans-square planar complexes.51 The atomic arguments made above imply that this - geometric peculiarity should not persist throughout the nickel triad. Palladium and platinum, being ground state dl0 and s1d9 atoms, respectively, should make covalent bonds - at roughly 90' to one another (i.e., cis square planar complexes). This should be particularly pronounced in palladium since the s2d8 state is so high in energy. Detailed studies have shown that bis(phenyldimethy1phosphine)- - dimethyl palladium prefers to adopt the cis orientation of the alky1,ligands by a factor of 7/3. 4 7 Thus, the prediction of geometry based on atomic states is verified, in a relative way, by comparing organometallic complexes of Pd(I1) and Ni(I1). These geometrical predictions have also been verified with ab initio electronic structure calculations. 52 Theoretical studies have predicted NiH2 to be a linear molecule with a 3~ ground state (characteristic of the s2d8 state of the nickel atom), and PdH2 to be a bent molecule (8 z 90°) with a 1A1 ground state characteristic of the s1d9 state of the Pd atom. 111. Hypothesis The above argument suggests that the driving force for the 0-alkyl transfer in (9) is the ability of the nickel atom to adopt the lower energy s2d8 configuration if the C-Ni-C angle is 180°, or, conversely, that the geometrical distortion of the C-Ni-C angle from the 180° optimum is energetically costly and the 0-alkyl transfer relieves the strain in the five-membered ring. The fact that the 0-0' carbon-carbon bond is cleaved rather than simply stretched is due to the facility of the 2 S + 2s reaction at nickel - recall the nickel valence d orbitals are already involved in the two nickel-carbon sigma bonds. It is apparent that the bis(phosphine)nickelacyclopentane, 4, is stable (vis-a-vis 0-alkyl transfer) because of the method of synthesis. This complex is prepared from the corresponding nickel dichloride - an inorganic complex which has previously coordinated (and static) phosphines. As the metallacycle is formed, the phosphines must adjust to accommodate the ring, and the metallacycle which is - isolated has the cis orientation of the phosphines. The stereochemistry of the complex is locked, owing to the observed inability of the coordinated phosphines to dissociate. 53 Thus, even though the 0-alkyl shift is thermodynamically favorable, it is kinetically forbidden. If the contention that the 6-alkyl shift is due to the 4s23d8 ground state of the nickel atom is correct, any nickelacyclopentane which is formed under circumstances which allow for the adoption of the trans geometry will do so, resulting in the production of ethylene as the primary decomposition product. In particular, if a bis(donor 1igand)nickelacyclopentane is formed in which the two donor ligands are forced to be trans, that nickelacycle should decompose to give ethylene. The attempt was made to prepare such a complex and study its decomposition. m. Transphos - 2,ll-bis(diphenylphosphinomethyl)benzo[c]phenanthrene Venanzi and coworkers have shown that the title ligand, .- transphos (abbreviated tp), 7, is an effective bidentate ligand, and that the chelating bite angle when it is complexed to a group VIII metal is 180°. 54 This ligand has been used byvenanzi and by Stille in complexes in which the trans orientation was desired. For this reason, we attempted This complex will have the desired trans orientation of the phosphines, allowing the C-Ni-C angle to open to the ms2d8n value. - The synthesis of 7 has been de~cribed,'~and the ligand was prepared by this route (Scheme 1). The only bothersome step in the process is the aromatization of the dibenzodecalin to the benzoIc1phenanthrene. ~enanzireported the use of DDQ in a minimum amount of benzene to carry out the aromatization. This procedure resulted in consistently low yields (42% reported by Venanzi). Our attempted aromatization by palladium in carbon in refluxing naphthalene was not successful; however, aromatization using $3CBF4 in acetic acid was quite convenient and yielded only two products (by NMR): 2.11-dimethylbenzoIclphenanthrene and triphenyl methane. Repeated crystallizations, chromato- graphies and sublimations failed to separate these compounds. This effort thus gave no better avenue to the desired product; however, it did lead to the discovery that the product is best isolated from the DDQ reaction by removal of solvent followed by sublimation (150°, 1 vm Hg) of the crude material. The rest of the synthetic sequence is convenient, giving an overall 5 % yield based on starting p-tolualdehyde. - V. Attempted Synthesis of (transphos)nickelacyclopentane, 8. A) Alkylation of (tp)NiC12 The dichloride of (tp)Ni is easily prepared. 57 The corresponding complex of palladium was alkylated by Stille with methyllithium to give (tp)PdMe2 trans stereochemistry. - presumably with the Treatment of tpNiC12 with excess methylmagnesium bromide resulted in a complex mixture of products (Figure 1). Owing to this and to the difficulty - anticipated in preparing 8 in this fashion, other syntheses ofbis(1igand)nickeldialkyls were sought. B) Exchange of transphos for bipy in (bipy)NiR2 Yarnamoto and coworkers have shown5' that the 2,2'- bipyridyl ligand can be replaced by chelating diphosphines in (bipy)NiMe2 (eq. 10) (bipy)NiMe2 + . For n-2 or 3 in eq. 10 42P(CH2)nP42 250 - 3p\ (CH2In NiMe2 + bipy \ / this reaction proceeds smoothly as shown, but for n=l or 4 reductive elimination of ethane resulted in the production of phosphine-stabilized Ni(0). We attempted the general- ization of this procedure shown in (11). The bipyridyl- stabilized nickelacycle has been rep~rted,'~and is quite easily prepared and handled. (10) Although the ligand replacement (eq. 10) occurs smoothly for (bipy)NiMe2, a similar ligand replacement is not facile for (bipy)NiEt2. 60 observed. Instead, reaction 12 is Therefore, it was necessary to check the (bipy)NiEt2 + - PCy3 1PCy3)2Ni(C2H4) + bipy (12) - feasibility of bipyridiyl replacement by phosphines in 9. The complex 11.2-bis(diphenylphosphine)ethane]nickelacyclopentane, g ,has been reported;41 therefore, reaction (13) was studied (dpe 2 1,2-bis(dipheny1phosphino)ethane). - Since 10 is slightly thermally labile, this reaction must proceed at room temperature or below if it is to be useful. This reaction did occur at a very convenient rate at room temperature in toluene. Treatment of 2 with 1.25 equi- valents of dpe at room temperature resulted in a change in sample color from the deep forest green of 2 to the bright yellow of almost immediately. -- conversion of 9 to 3 1 NMR ~ indicated the and a small amount of (dpeI2Ni. The ratio of 10 to Ni(0) was 17/1. Proton NNR is less useful in these complexes, but the proton NMR spectra for this reaction are consistent with the products shown. Further confirmation of eq. 13 comes from thermolysis of the products. 3 1 spectroscopy ~ indicated the conversion of 10 to ( d ~ e ) ~ Nafter i prolonged heating to 70". Reductive -elimination of cyclobutane has been reported for the thermal decomposition of XI, and cyclobutane is suggested in the proton NMR spectrum ofthisthermolysis. The proton NMR spectrum of the displacement reaction and of the thermolysis of the products indicates 1-butene also. This product is also reported in the thermal decomposition of 1,. (Attempted displacement of bipyridyl from (bipy)NiEt2 has resulted60 in the B-hydrogen decomposition to L2Ni(C2Hq). An analogous side-reaction in (13) would produce 1-butene.) We conclude that treatment of 2 with dpe results in the production of 2 and a small amount (<10%) of reduction to Ni(0). Reaction of $ with transphos was very sluggish. While the reaction with dpe was complete in less than 10 minutes, the reaction with transphos (eq. 11) was not obviously complete after 5 days. At the end of 5 days at room temperature, the proton NMR spectrum of a mixture of 9 and 1.5 equivalents of transphos showed a significant amount of - remaining and the only apparent organic product of the I! reaction to be 1-butene. The color of the reaction mixture changed very slowly from the dark green of 2 to a dark olive green ( $ 5 days) and finally to a dark red-brown (two weeks). After two weeks at room temperature, the - ~ spectrum having no free transphos, mixture showed a 3 1 NMR and only one significant peak. At this time, the proton spectrum of the reaction mixture showed a small amount of - 9 remaining, two peaks characteristic of the protons in complexed transphos, no ethylene, and a preponderance of 1-butene. - We conclude that treatment of 9 with transphos at room temperature results in the $-hydrogen decomposition to 1-butene and a transphos-complexed Ni(0) species. Reaction at below room temperature will be too slow to be conveniently observed and therefore this route to is not satisfactory. The production of 1-butene from this reaction is best explained by noting that the thennolysis of (Cy3P)Ni(CH2)4 yields 1-butene. If it is assume& that three-coordinate nickelacycloalkanes decompose via B-hydrogen pathways, the claim may be made that the 1-butene resulting from the reaction of transphos with 9 comes from a complex such as k&. The phosphine can displace the bipyridyl,5 8 ' 6 0 and this three-coordinate complex decomposes before the second phosphine can complex to the nickel. If this is the case, the ligand displacement reaction must be run at lower temperature. C) Synthesis of L2NiR2 from (pyrt4NiC12 + L + RMgBr It was recently reported" that L2Ni (CH2SiMe3) (L = two electron donor ligand) could be prepared by l ~ Me3SiCH2MgC1, and subsequently treating ( ~ y r ) ~ N i Cwith displacing the loosely coordinated pyridine ligands in (pyr)2Ni (CH2SiMe3) (eq. 14) features of this sequence: . There are four attractive (1) Although the ligand displacement was usually carried out at room temperature, in one case (eq. 14, L2 = dpe) this step was carried out at -30°C. The major drawback with the displacement of bipyridyl from 5 is the high temperature required. If the transphos ligand could be attached to the nickel complex at low temperatures, there is a better chance of isolating the transphos niekelacycle. (2) The displacement of pyridine ligands presumably occurs sequentially, hence if this process were used to prepare nickelacycloalkanes, it is not likely that three-coordinate species would be formed and 8-hydride decomposition would be suppressed. (3) Grignard reagents are used rather than the alkyl lithium reagnets which have been used to synthesize nickelacycles. Diqrignard reagentsG2 are much more easily prepared and handled than dilithium reagnets. (4) In common with route (B) (vide supra), in this process, the nickelacyclopentane is prepared before the trans-directing ligand is attached. If we know that the nickelacycle is intact before the ligand is added, we will obviously know the direct effect of the ligand additive. We tested the generality of this synthetic sequence by using it in the preparation of (bipy)NiMe 2' 63 (dpe)~i~e2,64 (bipy)NiEt234 and (bipy)Ni (CH2)4.59 since these compounds have all been reported independently, prepared by alternate routes, their preparation from (~yr)~NiC1* represnts a valid and simple test of the method. 1) Preparation of L2NiMe2 (L2 = dpe, bipy) The title dimethyl complexes of L2Ni for L2 = bipy and L2 = dpe have been prepared from Ni(acacI2 + A1Me2(OEt) + bipyridyl, and (dpe)NiC12 and methyllithiurn, respectively. We have prepared these complexes as in eq. 15. These reactions are best performed in tetrahydrofuran (pyr)4NiC12 + 2CH3MgC1 - - 1( p ~ r ) ~ N i M e=2 ~J L2NiMe2 (15) in view of the greater solubility of the digrignard reagents in this solvent,62 although in syntheses designed to isolate intermediate L? diethylether was used for easier solvent removal. The preparative reactions are performed at low temperature. Warming the reaction above O°C for prolonged periods (%15-30 minutes) resulted in the decomposition of the organonickel species to nickel black. Several equivalents of free pyridine were added at the outset of each synthesis. This presumably prevented the production of ligand-free NiMe2 (followed by decomposition). 61 Withholding of this pyridine did lead to the production of nickel black at lower temperatures. The ( p ~ r ) ~ N i C l ~ , excess pyridine, methymagnesium chloride and solvent were combined at -70°, the mixture was allowed to warm slowly to -20° and held at this temperature until the inorganic starting material was consumed. An excess of Grignard reagent was required; use of less Grignard resulted in excessive reaction times. The excess Grignard is necessarily quenched before addition of the replacement ligand (specifically in the case of bipyridyl). Isopropanol, water and trimethylsilylchloride were all used as quenching agents. Trimethylsilylchloride proved to be the most convenient in view of its volatility, but isopropanol was also practiced. Significantly, the replacement of the pyridine in (pyr),NiMe2 as -7a0! by bipyridyl was apparent at temperatures as low The (pyr),NiMe2 reaction mixture shows a bright orange to bright yellow color. When bipyridyl (2 eq. in thf) is added to this mixture (at -78*), there is an immediate color change which slowly gives complete predominance to the bright green color characteristic of (bipy)NiMe2. Although the kinetics of this process have not been studied, it is certainly apparent that this ligand exchange is synthetically useful owing to its tolerance for low reaction temperatures. NMR spectra of (bipy)NiMe2 and (dpe)NiMe2 prepared -. via 15 are shown in Figures 2, 3 and 4. In Figure 3 note the X2AA1X2' and X3AA1X3' patterns character is ti^^^ of the -CH2- and -CH3 protons, respectively, in (dpe)NiMe2. The 3 1 NMR ~ spectrum of (dpe)NiMe in Figure 4 is important, 2 because it indicates the virtual absence of Ni(0) products. 2) Preparation of (bipy)Ni (CH2) Complex g has been synthesized by a rather circuitous route," but not spectroscopically characterized. In Figure 5 we show the proton NMR spectrum of 2 prepared in this way, showing the two distinct protons of the metallacyclic ring. Integration shows the expected 1:l ratio, and decoupling irradiation (Figures 6 and 7) shows the coupling of the two proton sets. Integration relative to the bipyridyl resonances indicates the expected 2:4:2:4:4 ratio. This nickelacyclopentane can also be prepared by the method of eq. 14. Using 1.4-di(bromomagnesia)butane, ( p ~ r ) ~ N i Cand l ~ bipyridyl and the method outlined above, a complex was isolated whose H' NMR spectrum is identical to that of Figure 5 . Although the yield is low (lo%), the conditions have not been optimized and the literature preparation also results in a modest yield (21%). Most importantly, the result indicates the feasibility of this procedure for general synthesis of nickelacycles. 3) Isolation of (pyr),,NiMe2 The most convenient method for studying the formation and decomposition of 5 is NMR spectroscopy. It would thus be valuable to isolate the pyridine stabilized "naked" nickelacyclopentane as a solid. coworkers6' Carmona and reported the isolation and crystallographic characterization of ( P Y ~ ) ~ N ~ ( C H ~ T M Sthe ) ~ ,isolation of the corresponding dimethylnickel and nickelacyclopentane complexes appeared possible. The complex NiMe2-n(pyr) was isolated. Treatment of ( ~ y r ) ~ N i Cin l ~diethyl ether at -70° with 5 equivalents of methylmagnesiumchloride (as a thf solution) resulted in the production of a bright orange suspension in a red solution. This mixture was treated with several equivalents of trimethylsilylchloride to quench unreacted Grignard reagent. Filtration and repeated extraction of the solids gave a deep red solution. Removal of solvent and washing with pentane gave an ochre solid. Proton NMR (Figure 8 ) 65 shows resonances characteristic of pyridine (free and complexed) and a singlet at 6(-0.83). Treatment of this solid with bipyridyl in dB-thf gives bipyNiMe2. When the ochre solid and solid bipyridyl are placed in an NMR tube, even the solids mix and begin to turn green (characteristic of (bipy)NiMe2 ) . Solvent (dB-thf) is transferred onto this at -196O, and the color change to green is complete when the thf melts (-65OC). Thus, the ligand replacement reaction to give (bipy)NiMe2 is extremely fast. If a sample of the ochre solid in thf is kept at room temperature, there appears a good deal of brown-green precipitate and the resonance of 6(-0.83) in the proton NMR broadens and diminishes, the peak at c60.0 broadens, and a new peak at 60.85 appears. I interpret this as the reductive elimination of ethane and deposition of metallic nickel. These data indicate that the ochre solid produced in the above reaction is NiMe2.n(pyr). The value of n is difficult to determine since excess pyridine is necessary in the preparation of the complex. These data also indicate that for practical purposes the complex may be considered the functional equivalent of simple dimethyl metal. The pyridine ligands are so loosely coordinated that they are easily displaced even in the solid state. Although the analogous pyridine-stabilized nickelacyclopentane has not Seen isolated, there is no apparent reason to believe that it cannot be. These pyridine-stabilized nickel alkyls will prove to be very useful in organonickel synthesis. Structural characterization' and independent chemical studies will yield a good deal of information about the character of "ligand-free" metal alkyls. It is curious and unexpected that the complex (p~r)~Ni-Ms)~ is the only complex of the form LZNiRZ (in which L2 and R2 are - not chelating) which shows cis stereochemistry. 61 1t is not known whether this is due to selective crystallization, packing forces, etc., or to a distinct change in electronics about nickel. 4) Chemical studies should help explain this. Reaction of transphos with (pyr),NiRZ The reaction of transphos with ~iMe~.n(pyr)gave discouraging results. Treatment of the isolated organo- nickel complex with transphos is dB-thf led to the immediate (<20 minutes at -70°C) disappearance of the Ni-CH3 resonances in the proton NMR. Concomitant with this is the growth of a resonance at 6(0.86) which may be assigned to ethane. A new peak at 610.1 may be assigned to transphos bound to nickel. 57 After 8 hours at -70° and 15 minutes on +60°. the resonance at 6(0.86) is the dominant peak in the proton spectrum. This peak could be assigned to the Ni-CH3 resonance in ( t ~ ) N i ( c H ~ )but ~ , for the absence of the expected phosphorus-hydrogen coupling. These results indicated that it will be quite difficult to prepare organonickel complexes of transphos. Since the dimethyl nickel complex is so difficult to prepare, the metallacyclopentane complex is expected to be even more challenging. The obvious problem with this trans-directing ligand is its great bulk. It must be that the ligand displaces both pyridine units before complexing both phosphorus atoms to the metal. In future work, I suggest either performing the preparative ligand exchange reactions in neat pyridine or use of a different trans-directing ligand. pyridine will cause trouble: Use of neat (1) the high melting point forbids low temperature reactions, 12) the high boiling - point makes removal difficult, and ( 3 ) unless all of the pyridine is removed from the reaction medium, there will still be ambiguity in assignment of the active nickel species in the reaction. Replacement of the four bulky phenyl rings in transphos with methyl groups provides an attractive alternative trans-directing ligand. The "tetramethyl transphos" will be able to complex more easily to the nickel atom, allowing the ligand displacement to proceed at lower temperatures. Finally, there will be the obvious technica1,benefit of having the molecular weight of the trans-directing ligand reduced by 50%. VI. Conclusions The force behind and mechanism of the 6-6' carbon-carbon bond cleavage reaction in the organic chemistry of nickel is still not understood. The possibility of stereoelectronic control in organometallic chemistry is very attractive and must be more thoroughly investigated. The carbon-carbon bond cleavage reaction in nickelacyclopentanes may be an example of a reaction which is so-controlled, but the question is technically difficult to answer. Alkyl complexes of nickel whose stabilizing ancillary ligands are pyridine have been prepared, isolated and used in the synthesis of organonickel complexes having more complicated ligands. These ligand-replacement syntheses proceed at very low temperatures and are quite convenient. Generalization of the process described here will allow the formation of a variety of complicated organonickel complexes which have not been prepared to date. 66 Experimental All operations involving organometallic complexes of nickel were carried out either in vacuo or under inert atmosphere. ~oluene,diethyl ether, tetrahydrofuran, benzene and all hydrocarbon solvents were dried over sodium benzophenone ketyl and vacuum transfer distilled before use. Pyridine was dried over calcium hydride. Ni(COD)2 was either prepared via the published procedure,62 or purchased from Strem Chemicals and used without further purification. Tetrabis(pyridine)nickeldichloride was prepared as in the literature,68 as were the bis(phosphine)nickel dihalides used in this study. 67 1,4-dichlorobutene and l,4-dibromobutane were dried over Linde 4A molecular sieves and vacuum-distilled before use. 2,2'-bipyridyl and 1,2 bis(dipheny1phosphino)ethane were purchased (Aldrich Chemicals and Strem Chemicals, respectively) and used without further purification. Unless otherwise noted, all spectra were recorded at room temperature. 2,ll-bis(diphenylphosphinomethy1)benzo[c]phenanthrene (1) This compound was prepared via the literature route, although the following modifications of the aromatization step were attempted. 11 Aromatization with palladium on carbon. 70 1.0 g (3.8 mole) of 2,ll-dimethyl-5,6,6a,7,8,12bhexahydrobenzoIclphenanthrene, 17 g of naphthalene, 100 mg of palladium on carbon and 5 equivalents (based on hydrocarbon) of indene were refluxed (21E°C) for 20 hr. Thin layer chromatography (silica plates; pentane elution solvent), and proton NMR showed no aromatization at all. 2) Aromatization using triphenylmethyl cation. I I 1.0 g (3.8 mole) of 2,ll-dimethyl-S16,6a,7,8,12bhexahydrobenzo[c]phenanthrene and 1.5 g triphenylmethyl- tetrafluoroborate were refluxed in glacial acetic acid until the initial yellow-brown reaction color is replaced with a bright burgundy and TLC indicates the absence of starting hydrocarbon. The reaction mixture was poured into water and extracted with benzene. The benzene extract was thoroughly washed and dried over MgS04. Removal of solvent gave a crystalline solid which proved (by NMR) to be a mixture of triphenylmethene and the desired aromatic produced. Crystallization from benzene/ethanol (1:l) removed a good deal of $3CH, but left a mixture of the two products of ~ 1 : lratio. Chromatography (diethyl- ether, or benzene, or pentane or pentane/diethyl ether as eluting solvents) gave no separation at all. The two products co-sublime, thus sublimation/distillation was not effective in separation. Crystallization from ethanol, pentane, petroleum ether, diethyl ether, benzene or toluene gave little success. A low temperature crystal- lization from toluene gave a mixture of triphenylmethane/ dimethylbenzoIclphenanthrene of 1/3 (NMR). Separation not being fruitful, the triphenylmethane impurity was carried through the bromination step. Unfortunately, fickle bromination of the dimethyl hydrocarbon to give -CHBr2 and -CH3 are serious side reactions and accurate use of NBS is necessary, thus triphenylmethane (which is also brominated) led to a mixture of bromination products. Even though the aromatization went to apparent completion, this method is not useful. (2,2'-bipyridy1)nickelacyclopentane This synthesis follows the method of Hagihara and coworkers. 3a 5.0 g (18 mMole) Ni(COD)2 and 5.7 g 2,Z'-bipyridyl are degassed in a schlenk vessel. cold (0') 75 ml THF is added, resulting in a fast (but not immediate) ligand replacement to give soluble, purple (bipy)Ni(COD). After all of the Ni(COD)2 has reacted and the nickel species dissolved, 1.35 ml (2.4 g, 11 M o l e ) l,4-dibromobutane is added all at once to the mixture. This mixture is stirred at 0' for approximately 3 hr. At this point, the purple solution has turned green and a good deal of precipitate (pink-colored (bipyI3NiBr2) has separated. The solvent is removed (in vacuo, O°C) to give a grey solid. This solid is washed with several aliquots of cold n-pentane to remove excess dibromobutane. 72 The resulting grey solid is extracted with fresh tetrahydrofuran until the extracting solvent is colorless. In the absence of excess alkyl halide, the nickelacycle is stable at xoom temperature. Removal of solvent gives a powder which is crystallized from THF/pentane to give dark green (black) crystals. Recrystallized yield 500 mg (21%). Spectra of this material are shown in the text. Reaction of (bipy)Ni(CH2i4 with 1,2-bis(diphenylphosphin0)ethane (dpe). In an NMR sample tube, 12 mg (44 mole) (bipy)Ni (CH2) and 22 mg (55 mole) dpewere added to 300 111 dry toluene-dg at room temperature (sample prepared in an inert atmosphere box). There was a quick color change from green to yellow. This reaction seemed to be limited by the rate of dissolution of the fairly unsoluble organonickel complex. After 15 minutes at room temperature, H' and 3 1 ~spectra were recorded. The proton spectrum showed free bipyridyl, free and complexed dpe (P-CH2 at 62.11, peaks at 61.85 and 61.67 which have been assigned41 to and peaks in the alkyl the ring protons in (d~e)Ni(cH~)~, and vinyl regions consistent with 1-butene. The (proton- decoupled) 3 1 ~ NMR spectrum shows free phosphine, and (dpe)2Ni (0) and (dpe)Ni(CH2) in a ratio of %20:1. These resonances are consistent with those of independently (from Ni(COD)2 and dpe) prepared samples of (d~e)~Ni(O) and (dpe)Ni(CH2) . (from dpe)NiC12 and l,4-dilithiobutane) Thermolysis of this sample (+70°, 36 hours) gave complete conversion to (dpe12Ni(0) (31P NMR). The protons in cyclobutane (the reported organic product of themolysis), the ethylene protons in dpe and the methyl protons of toluene appear at % 62.0 in the proton NMR so assignment of the organic products of this decomposition is not possible using proton NMR, but the resonances assigned to the ring protons in (dpe)Ni(CH2Iq are absent in the themolyzed sample. Reaction of transphos with (bipy)Ni(CH2L2 Transphos (1; 36 mg, 58 mole) and ( b i p ~ ) N i ( C H ~ ) ~ (8 mg, 30 1.1Mole)were added to an NMR tube (sample prepared in inert atmosphere box). Tetrahydrofuran-d8 (0.5 ml) was vacuum-distilled into this tube which was subsequently sealed. Immediately upon the melting of solvent, the 3 1 ~ and 1H NMR spectra were recorded. The 3 1 spectrum ~ showed a large peak (free transphos) plus a small impurity (the phosphine-oxide) in a ratio of 220:l. The proton spectrum showed only unreacted starting materials and a small unidentified impurity at 6(0.13). The reaction was monitored periodically for two weeks, during which time the color of the reaction mixture changed very slowly from bright green to red-brown. a new resonance in the 3 1 At commensurate rates, ~ (20.5 - ~ ppm ~ ~downfield from free transphos) and resonances due to 1-butene in the proton NMR appear. (A third 3 1 ~resonance (34.3 ppm downfield from free transphos) appeared after the first day of reaction, but did not grow in size and represented only -3% of the entire phosphorus spectrum, hence it is unimportant.) During the course of two weeks, the signal due to free transphos both broadened and lost intensity until it disappeared altogether. At the end of two weeks, no free phosphine was observed in the 3 1 NMR ~ and only a small amount remained in the proton NMR. At this time, the proton NMR showed small peaks due to (bip~)Ni(CH~)~ which remained, a large amount of 1-butene and a new broad peak in the alkyl region which is relatively small and may be assigned to n-butane. This reaction is therefore not of synthetic utility in this case. Preparation of. (bipy)NiMe2 from (pyr) NiC12 and methyl4magnesium halide. Tetrabis(pyridine)nickeldichloride (1.0 g, 2.2 mMole), 20 ml dry THF and 4 ml dry pyridine were added to a schlenk vessel which had previously been purged with argon. suspension was cooled to -70°C. The Slowly (over the space of 3-5 minutes) 11 ml of a 0.64 M THF solution of methyl- magnesiumchloride was delivered (via syringe) into the reaction vessel. There was an immediate color change from aquamarine to pale yellow-green. The reaction was allowed to warm to -20°C which vigorous stirring was maintained. The reaction was stirred at -20" until the inorganic starting material was no longer evident. rich orange-colored suspension. This gave a The mixture was cooled to -70° and 230 ul degassed isopropanol was added to quench any unreacted Grignard reagent. Stirring was maintained until gas-evolution ceased. 2'2'-bipyridyl (0.6 g; 3.8 m o l e ) was degassed, then Sissclved in 5 ml dry tetrahydrofuran. This solution was cooled to -40" and then transferred via syringe to the (pyrInNiMe2 reaction mixture which was kept at -70°. Immediately a color change was apparent. The -70' bath was replaced with a -20° bath and the reaction mixture stirred at this temperature until the color change was apparently complete (1-2 hr). The solvent was removed in vacuo from this green suspension. The bipyNiMe2 was extracted from the resulting grey solution with 20 ml refluxing benzene. Hot filtration gave a dark green homogeneous solution from which purple-black needles form. (% After cooling +lo0) the crystalline product was isolated and washed several times with n-pentane and dried in vacuo. Recrystallized yield 116 mg (22%). Proton NMR in acetone-d6: 67.65 (inteqral = 2.0, bipyridyl), 68.2 (integral = 4, bipyridyl), 69.05 (integral = 2, bipyridyl), 60.0 (integral = 6, Ni-CH3). Preparation of (dpe)NiMe2 from (pyr)4- NiC12 and methylmagnesium halide. The same procedure was used here as was used to prepare (bipy)NiMe2, the only change being that, owing to solubility the dpe ligand was added to the [(pyr),NiMe21 as a solution in toluene rather than thf. The crude material was purified using the literature procedure. 64 This resulted in the isolation of 210 mg of material whose spectra were identical to those of independently prepared dpeNiMe2 and (dpeIZNi. The dpeNiMe2 was contaminated by 10% with (dpe)2Ni (based on 3 1 NMR) ~ . Preparation of (bipy)~i(CH~l~ from (pyr)4-NiCl ---2- and Di-Grignard reagent. The preparation of 1,4-dibromomagnesiumbutane followed literature methods. 48,62 Tetrakis(pyridine)nickeldichloric¶e (1.0 g, 2.2 Mole) was suspended in 15 ml tetrahydrofuran and 2 ml pyridine. This mixture was cooled to -70'. A solution of 1.4- dibromomagnesiabutane (33 ml, 0.1 M solution) was added slowly to the well-stirred suspension. allowed to warm slowly to -lo0. The reaction was When all of the (pyrI4- NiC12 had reacted, the mixture was cooled to -70° and 180 u1 degassed isopropanol was added. A solution of 0.7 g bipyridyl in 5 ml tetrahydrofuran was added to this cooled mixture which was subsequently allowed to warm to -30° until the color change (orange-to-green) was complete. Most of the solvent was removed in vacuo at room temperature. The resulting slurry was washed with 2x50 ml dry pentene. The dried solid was extracted with toluene at +40° until the extractions were colorless. The solvent was removed from this extracted material. Two recrystallizations (toluene/pentane) gave 60 mg (10%) (bipy)Ni (CH2)4. This sample gave proton spectra identical to the material prepared from Ni(COD)2, 1,4-dibromobutane and bipyridyl. Attempted preparation of (bipy)NiEt2 from (pyr)4-2-NiCl and ethylmagnesium choriate. The preparation of (bipy)NiEt2 using the ligand replacement on (pyr),NiEt 2 was attempted several times. In each case a procedure similar to that described above for (dpe)NiMe2, (bipy)NiMe2 and (bipy)Ni (CH2) was used, with small variations. In each case, the ligand replacment appeared to proceed properly, giving the expected orange-to-green color change. In each case, however, decomposition to a pale brown material occurred during the work-up of the reaction. The green suspension is stable, even at room temperature; therefore, the - product is isolable, but appears to be much more sensitive than the dimethyl complex. Reaction of methylmagnesium bromide with tpNiC12 The synthesis of (tp)NiC12 is reported. 57 A suspensian of this material (100 mg, 0.13 mMole, in 5 ml tetrahydrofuran) was cooled to -60°. Methylmagnesium bromide (1.6 ml of 0.64 M solution in tetrahydrofuran) was added over 10 minutes. The mixture was stirred, warming slowly to room temperature. The purple suspension reacted to give a bright red solution. When no tpNiC12 was apparent, the mixture was cooled to -60° and 60 ul of degassed isopropanol added to quench the excess Grignard. Solvent was removed to give a sticky orange solid which was extracted with 5 ml benzene. This extract was filtered through a celite pad to give a clear homogeneous red-orange solution. powder. Removal of solvent in vacuo gave a vermillion ~ spectrum of this powder The H' NMR and 3 1 NMR are shown in Figure 1. Preparation of (pyr)nNiMe2 Tetrabis(pyridinefnickeldich1oride (1.0 g, 2.2 mMol) was degassed in a schlenk vessel. Solvent ( 7 5 ml diethyl ether/? ml pyridine) was added to this. The suspension was stirred and cooled to -40a. Methylmagnesiumchloride (4.0 ml of a 2.9 M solution in tetrahydrofuran) was added dropwise to the mixture. After the addition was complete, the mixture was warmed to Oa and stirred vigorously until the ( ~ y r ) ~ N i Chad l ~ reacted (circa 3 hr). The mixture was cooled to -lo0 and 2 ml of dry (sieves), degassed trimethylsilylchloride was added. After stirring for 15 minutes, the mixture was filtered under argon through a chilled frit. This gave a red-orange solution and a very pale solid. The solid was extracted once with 25 ml diethyl ether/5 ml pyridine. Filtration and combination of filtrates gave a bright orange solution and colorless powder (MgX2, discarded). The solvent was removed to give a pasty yellow-red solid. washed with pentane (0') This solid was and dried in vacuo. NMR of this product is shown in Figure 8. The proton Figure 6. Spectrum from F l g u n 5. H e n the signal s t 61.89 was decoupled front the remainder of the spin system. F i g m 8. 'H rpectnr (JEOL FX-900, %-thf solvent) of (pyr),llimZ. All shifts a n relatiw to Vn nsldual protons in the r o l m t . Sipnal a t 19.0 are dw to s i l y l impurities r-inlnp after the m C1 qwnch. REFERENCES 1. P. W. Jolly and G. 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L. Beauchamp, - Organmetallic, 1982, & r 963-968. The kinetics of this process have been described. K. C. Ott, personal cormnunication. F. Ozawa, A. Yamamoto, T. Ikariya and R. H. Grubbs, Organometallics, 1982, 1, 1481-1485. (a) J. X. McDermott, J. F. White and G. M. Whitesides, J. Am. Chem. Soc., kg=, 98, 6521-6528. (b) G. B. Young and G. M. Whitesides, J. Am. Chem. Soc., --. 1978, 100, 5808-5815. C. E. Moore, "Atomic Energy Levels", National Bureau of Standards NSRDS 35, Government Printing Office, Washington, D.C., 1971. F. A. Cotton and G. Wilkinson, "Advanced Inorganic Chemistry", 4th Ed., Wiley-Interscience, N.Y., 1980. Reference 1, Volume 1, Chapter 4; see reference 6 for the only exception. (a) M. L. Steigerwald and W. A. Goddard, III., unpublished results. (b) M. Blomberg, U. Brandemark, L. Petterson and P. Siegbahn, personal communication. The 3 1 NMR ~ spectrum of a mixture of bis(tripheny1phosphine)nickelacyclopentane and free triphenyl shows no exchange of phosphine between the two sites. 52, (a) L. M. Venanzi, Pure and Appl. Chem., 1982, 1117-1129. (b) F. Bachechi, L. Zambonelli and 60, 2815-2823. L. M. Venanzi, Helv. Chim. Acta, 1.977, A. Gillie and J. X. Stille, J. Am. Chem. Soc., 1980, 102, 4933. N. J. DeStefano, D. K. Johnson, R. M. Lane and L. M. Venanzi, Helv. Chim. Acta., 1976,2, 2674-2682. N. J. DeStefano, D. K. Johnson and L. M. Venanzi, -- Helv. Chim. Acta., 1976, 59, 2683-2690. T. Kohara, T. Yamamoto and A. Yamamoto, J. Organomet. Chem., 1980, 192, 265-274. -M. J. Doyle, J. McMeeking and P. Binger, J. Chem. Soc., -- Chem. Comm., 1976, 376-377. E. Dinjus, I. Gorski, E. Uhlig and H. Walther, 2. -- - Anorg. Allq. Chem., 1976, 422, 75-79. E. Carmona, F. ~onz&les,M. L. Poveda, J. L. Atwood and R. D. Rogers, J. Chem. Soc. Dalton, J,93, 777-782. (a) C. D. Nenitzesen and I. Necsoiu, J. Am. Chem. Soc., - .-. 72, 3483-3486. 1950, (b) I. T. Millar, H. Heaney, - Quart. Rev. Chem. Soc., 1952, 11, 109-120. G. Milke and G. Herrmann, Angew. Chem. Int. Ed. Enql., 1966, 5, 581. M. L. H. Green and M. J. Smith, J. Chem. Soc. ( A ) , --, 1971 639-641. The multiplet at %6(0.0) is due to unremoved silyl products of the trimethylsilyl quench. Later studies found these contaminants to be innocuous and easily removable. (a) J. W. F. L. Seetz, F. A. Hartog, H. P. Bijhm, C. Blomberg, 0. S. Nekerman and F. Bickelhaupt, 23, 1497-1500. Tet. Lett., 2 8 2 , - (b) L. C. Costa and G. M. Whitesides, J. Am. them. Soc., 19=, 99, 2390-2391. 67. Reference 3b, p. 178. 68. F. Reizenstein, 2 . Anorg. Chem., 1896_, 11, 254. 69. (a) L. M. Venanzi, J. Chem. Soc., - 1958, 719-724. (b) C. R. C. Coussmaker, M. H. Hutchinson, J. R. Mellor, L. E. Sutton and L. M. Venanzi, J. Chem. Soc., 1961, 2705-2713. (d) P. J. Stone and 2 . Dori, Inorg. Chem. - - Acta, 1971, 5, 434-438. 70. P. P. Fu and R. G. Harvey, Chem. Rev.. && ' @, 78, 317-336. 71. P. P. Fu and R. G. Harvey, Tet. Lett., _1974, 3217-3220; and references. 72. Complexes of the form (bipy)Ni(Rl)(R2) are known to react with R'-X to give R1-R' and R2-R'. (a) S. Takahashi, Y. Suzuki, K. Sonogashira and N. Hagihara, J. Chem. Soc., Chem. C m . , (b) Reference 7b. at O 0 1 9 7 6 , 839-840. This reaction is observed to proceed - 25O; hence, the preparation of (bipy)Ni(CH2I4 from Ni(CODI2 and Br+CH2j4Br is something of an art. 73. Failure to quench the Grignard reagent is particularly when bipyridyl is introduced to the detrimt?nta.l reaction, owing to the rapid formation of the radical A anion Ibipy] 222, C17-C20. - . (a) W. Kaim, J. Organomet. Chem., 1981, (b) E. C. Ashby, A. B. Gock and R. N. DePriest, J. Am. Chem. Soc., 1980, 102, 7779-7780. Chapter 7. Concerning the Mechanism of ZieglerNatta Polymerization nf simple D i d i n s pG. pmb .&md - at tk m h h r kd -L ~ l . ~ k ~ a m d**Lpnr101 t ~ t ~ ~ dMIp~mbn b.on for ilu la L(bbm.4, L l b l h . 4 . Y,*tuo .Ld daRn h&nm$.lh imm a m l a k TI. d a A 1LL d h . ~ r u n n ti UI nr). md. d o r b o n ~ r b o nbond f a ~ t bM .o 1 (lba mhk diai& bal~l. a d wibii. clruudn.rkllirnankdd~d.lthhwsnd.l.nd . I.. iu demwyvprcldikpolynrrivlapcrorvmuubudaC.. C, 1.1) 111 1.01 lun(. 1.55 1.24 0.89 T . o d t k m s d r r ~ l y ~ m d ~ k u m n ( ( & m n y ~C,. C. 1.21 I 0.17 -ld . n c b . urbau.l.%mullaqck n r h s n i u d G m a C~ ,dl a* a d Romey' ( S s b I.a) and tb. d i m fo.,-xnlnM i a inunip, - b n h d bu rd A r t m a (Scknr I. b)? Neitbn d t k . . w h k iaraMktat with UI k a n n W - d *hr '* ....-- ..-- , .... 1.31 ,r. 1.06 0.11 017 adamdmiaI.yanrdU.-'~dtnornmniar hehndtd.rmodaia j d f ~ d a t r p d b a h p c Tkh~(udilr~ba.PnI*mypUr b UI islalrarnl d brdrpra m i m l a is a (SEknc I). Tbu mohbt) tmpllo a h r i c P ~ I immr ) &opr .nm on cham w*' - l m p p t a m . a d n L t d ~ a b r l o p r h d n m b In our dm to & n m r dn m a - s R n Ihu m m p l - ., u!., by~a.lum~nunaIbyln b) I*f - l a d ' TI. Cp,TkHfiI(CHl)F lrmn Cp,TCI, and ICH,I,AI u*oprdolIorIb"rmoa.l Olht&ld~lhl~lau I.Uba-3.dI5" E-Ktkrb@qnmt#nlplm -3 h ~ * a a p n d t k n ~ ~ l r p . t k m m d . p -mkd-'nLLN,mY* l ~ ms npad d r ) U o p r d m 1- mnm m d n q tc umwulg TI. l.ood.r) -,7, e h.rolrdu(bou~pmrmh~.naym1i-I1wII 6- Irr mdeb -I f a d s m awnlo uto a mmakrbm b,d- " *? - L' ",: i.CLy Y ~ m Ce.7 - C M l ~ ~ c u"uoa.rw @ . ~ I ~ ' t CpII.-C*O t lI)CIP.J.W).uJ,DP i h L J . W W J , I C * . ~LJ;CI1.P.lMIUJ,)IU (21 - . L . J . J QI ~ r . m . nr.alm rn n*ur~.nbh"..ldnn r q )*..r.mIl =c,c.,..,.~Y~-. IN(.IUI X-W~>.Y o M K. J S J .$2 ~mC. @;am. L.n.:w.*u ~~.~k.k,.~k.-~mreuo,a-u.~n.m *IZ m.nla n-as. ...~-.~ ) ~ ? . Y ~ ~ c E . ~ C I ~ M . Z Z ? ~ * ~ * . l4IL.ll.lCYYnUI i.Y.rk "-,a. *IY..H;-II.W.Y.OC~.~.C~ *dl. 1)).18.)11)). Vll4LR;~La.J.r..Plr&.IIL).).II).1Ik ww. mi. mj-ma. (IlYrkJ.Y;W*r.D.B;Lrr,l.D;kr.J.LJ. r ~ .Q*, . k.n im ntcm. mw*r.?.LJ.r~..~.k.h- 0WT-P.W;-O.W.J.rL..Ck.&.~.PJ. mm. (lllo.clrLA;DnrYI**?.L~.*v~*Y YI*r.4 tU 1. I+&*. IIIIQL-IIIL I ~ - L L ~ . ~ . L ; ~ , ~ z . R . &th durin* t k ndeumiiw U s p d p q . p t & . 6 b pPib*lpIlkyaintoL~&imiinunniyrith~brid~ acd srntcr rhkh hnol bn llr aulw dl* ddrrin* M t i o a a tho1 I& ..CH0 an oiwp ~modw~nltbs r u t mta. S r b .g.U nol . ~ ~ . r i lh Y .IMope d m bul auld hrr a -d inllvrnn a tlr ~eurrsas- - he probability of propagation to a chain of N links before teraination is given by that is, N-1 propagations (1) and one termination + a given time, a s r u m ~ n equilibrium of steady state is achieved, the number average egret of polymerization is given by At define r - (= 7 5) Set A.1. and 1 N r N- l an& an arbitrary variable 1 . ) This result agrees with that predicted by standard methods. N w consider the co-polymerization of two species: a deuterated and an undeuterated monomer. The fate of growing chains depends on the nature of the terrinal unit, so split the problem to a consideration of each case: H-terminated and D- - terminated growing chains N N-link chain which is D-terminated, PH N [PD - N-link chain. H-terminated). Each chain can either grow or terminate (temporarily ignore isotope effects on complexation). termination temination -' !k k~ :P P; - - pN+l k~ We know that rH = rate of propagation past aa H-terminus 9 ,k (pH) (olefin) ry = rate of chain transfer at m H-terminus !k (pH) (olefin). Similarly kD r; - kg (PD) (olefin) k; ( P ~ )(olefin). The probabilities of a given H-rxn (i.r.,.H-terninus reaction) being propagation or temination are T rH * rH - k H + ) -H and IT T~ + respectively; and similarly for D-rms. The probability of a given reaction being an H-rxn is simply Similarly for aD (= prob. that a rxn is a D-rxn). vH H "T - So w e have prob. that a rxn is a propagation past am H-terminus = probability that a rxn is termination after an H-terminus and Nor is is assumed that the ratio of the concentration of Dterminated chain (growing) to H-terminated is a constant (call it C ) . So the probability of terminating a chain by chain transfer after an H-monomer terminus after trowing a chain of N units, n of which are D is similarly for transfer after 8 D terminus: e: ) D ~1 h- (r;-l rfn ):. Thus the probability of generating a chain N units long, n of which are deuterated is given by: - H~Yn) D~Yn) N '(n~ + In order to simplify, note that r,+ - (PHI 7(kH) (P,) (PHI rH T - . It--)!k( where R so, - H (kH + kT) (PHI 7 (kD) rp r + PA) - (;)N(~(P~)L~IN-~-~ - (P,) ):k( D (PD) (kD + kT) i (pD) (kD)ln-l) (r~~)(~~)[.~g (Wil) k& - (iIN [pDln (pH)*-. (kt-' k;-'-l + pDq(*;I) 'Hk; k:$) In this form, the relationship of tq"(2) It only remains to be shown that to tqul is ) obvious Thus Thus equation (2) represents the generalization of equation (1) to the case of two component polymerization, if the new definitions are made That is, Then, summing on n for a given N and determining the average N (S <N>), Now find cn> as function of N 276 here .en [ - (I-B)(~-~)-~ e (N-I) (8) n 1 * - ck; fT so Rec*ll i t - 5 , . q * c(kD $1 - k,* t1 Therefore <,,, . (+' ["*.)"-' k (p kq )~ ; j [(a) . ra: c] ;~ For a given N , the d i s t r i b u t i o n o f n i s given by i s defined ( a s e a r l i e r ) a s where FN (n) No* define a. So define 2 and,. ck; Here N represents the wmormelized distribution of n. Examples Suppose c-1, end let: Let H - " - IrDq - 0.9 and B -$- 8 Distribution for C-1. a-0.9. 0-2 and N-20 2.0 CONCLUSION In this thesis the results of a study of the suprafacial 2 + 2 reaction have been presented. The electronics of the transformation have been described in terms of the motion of four singly-occupied electronic orbitals. If these orbitals are able to change their shapes in continuous ways from reactants to products, and if these shape changes do not result in the cleavage of either of the two active bonds (as judged as orbital overlaps), then the suprafacial reaction can occur. The stipulation that both bonds be retained during the entire reaction engenders severe restrictions. In the nonpolar four-center process, the participation of an orbital which is antisymmetric with respect to the reaction is demanded. The energy of this orbital and its ability to form a covalent bond which is antisymmetric with respect to the reaction determine the energetic barrier to the electronic reorganization implied by the 2s + 2 s reaction. One very common example of the 2s + 2s reaction is the organometallic migratory insertion reaction - a cornerstone in the chemistry of homogeneous catalysis. The principle of maximum bonding upon which the Woodward-Hoffmann rules are based, coupled with the description of the migratory insertion as a concerted process, and the notion that a given ligand environment around a given model supports one state of covalency at the expense of the alternatives suggests a simple rule for the design of homogeneous catalysts. During a homogeneously c a t a l y t i c c y c l e , t h e number of c o v a l e n t bonds t o t h e m e t a l a t t h e a c t i v e s i t e of t h e c a t a l y s i s s h o u l d remain c o n s t a n t . bdi et amo! QpvLe i d ~aoidm@ M u s e hecjuinib. Nebcio, bed d.L&I d e n t i a et e x o t u c i o ~ .